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Properties

Label 27930.x
Number of curves $1$
Conductor $27930$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("x1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 27930.x1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 + T\)
\(5\)\(1 - T\)
\(7\)\(1\)
\(19\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 5 T + 11 T^{2}\) 1.11.af
\(13\) \( 1 + T + 13 T^{2}\) 1.13.b
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(23\) \( 1 - T + 23 T^{2}\) 1.23.ab
\(29\) \( 1 - 4 T + 29 T^{2}\) 1.29.ae
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 27930.x do not have complex multiplication.

Modular form 27930.2.a.x

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} + 5 q^{11} - q^{12} - q^{13} - q^{15} + q^{16} + 6 q^{17} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 27930.x

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27930.x1 27930r1 \([1, 1, 0, -3695905122277, 2735775223839669901]\) \(-138357846491853121383730987168838623/55816105091607428996184145920\) \(-2252381169137425187992419524086333440\) \([]\) \(957640320\) \(5.9387\) \(\Gamma_0(N)\)-optimal