Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} - 49x $ |
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This modular curve has infinitely many rational points, including 2 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map
of degree 24 from the Weierstrass model of this modular curve to the modular curve
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle -\frac{2^6}{7^4}\cdot\frac{57576232x^{2}y^{14}-7756878640x^{2}y^{13}z+1136483432506x^{2}y^{12}z^{2}-326259862656000x^{2}y^{11}z^{3}+121445703987160784x^{2}y^{10}z^{4}-6820377070971912840x^{2}y^{9}z^{5}+189789127309741608663x^{2}y^{8}z^{6}-4129027352021232142720x^{2}y^{7}z^{7}+86445613300453399342840x^{2}y^{6}z^{8}-1496734069936686941141040x^{2}y^{5}z^{9}+18157946354796971325469965x^{2}y^{4}z^{10}-144279875233475020436887840x^{2}y^{3}z^{11}+716080195850326077940474200x^{2}y^{2}z^{12}-2024616305116531413993930280x^{2}yz^{13}+2498148468296656122838172835x^{2}z^{14}+4606760xy^{15}+1502590964xy^{14}z-202968021280xy^{13}z^{2}-12458476253776xy^{12}z^{3}-6410289876945360xy^{11}z^{4}+750315021769423635xy^{10}z^{5}-63911064290427174240xy^{9}z^{6}+2905635495382262419504xy^{8}z^{7}-73300011342381992835240xy^{7}z^{8}+1105724028524763422093312xy^{6}z^{9}-10304417587885144337489120xy^{5}z^{10}+58465093326465929497880360xy^{4}z^{11}-185892891061440833349656920xy^{3}z^{12}+254984384409240407168601837xy^{2}z^{13}+148877y^{16}+421947680y^{15}z-84752047744y^{14}z^{2}+22041002592560y^{13}z^{3}-843648349584180y^{12}z^{4}-364903318435759040y^{11}z^{5}+28377344717055167960y^{10}z^{6}-887669437268695622520y^{9}z^{7}+15034134431156082039980y^{8}z^{8}-150295035200208379943840y^{7}z^{9}+893515314749506508133088y^{6}z^{10}-2956826260013998683903480y^{5}z^{11}+4211297312230736459729158y^{4}z^{12}+687105339718766803308320y^{3}z^{13}+4594138036157089615560232y^{2}z^{14}+18011607213770166024611240yz^{15}+28522038984244586076777677z^{16}}{408x^{2}y^{14}-149718562x^{2}y^{12}z^{2}-15020539728x^{2}y^{10}z^{4}+11312588574861x^{2}y^{8}z^{6}-869665601010360x^{2}y^{6}z^{8}+22871143825881855x^{2}y^{4}z^{10}-114348410082341400x^{2}y^{2}z^{12}-2760161048458211055x^{2}z^{14}-63812xy^{14}z+1465928912xy^{12}z^{3}-462127976223xy^{10}z^{5}+43542994634832xy^{8}z^{7}-2103602264629376xy^{6}z^{9}+58460614273631640xy^{4}z^{11}-760402684363040481xy^{2}z^{13}-y^{16}+4651136y^{14}z^{2}+2590036484y^{12}z^{4}+2599738303848y^{10}z^{6}-825705952864604y^{8}z^{8}+63958118192243744y^{6}z^{10}-2122001290745474334y^{4}z^{12}+32555244649425696408y^{2}z^{14}-191581231380566414401z^{16}}$ |
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Cover information
Click on a modular curve in the diagram to see information about it.
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This modular curve minimally covers the modular curves listed below.
This modular curve is minimally covered by the modular curves in the database listed below.
