Properties

Label 277200.fa
Number of curves $1$
Conductor $277200$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("fa1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 277200.fa1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1\)
\(7\)\(1 + T\)
\(11\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(13\) \( 1 + T + 13 T^{2}\) 1.13.b
\(17\) \( 1 - 4 T + 17 T^{2}\) 1.17.ae
\(19\) \( 1 + 3 T + 19 T^{2}\) 1.19.d
\(23\) \( 1 + 6 T + 23 T^{2}\) 1.23.g
\(29\) \( 1 + 7 T + 29 T^{2}\) 1.29.h
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 277200.fa do not have complex multiplication.

Modular form 277200.2.a.fa

Copy content sage:E.q_eigenform(10)
 
\(q - q^{7} + q^{11} - q^{13} + 4 q^{17} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 277200.fa

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277200.fa1 277200fa1 \([0, 0, 0, -383925, -91564625]\) \(-34339609640704/916839\) \(-167093907750000\) \([]\) \(1612800\) \(1.8341\) \(\Gamma_0(N)\)-optimal