Properties

Label 51520bl
Number of curves $1$
Conductor $51520$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 51520bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51520.m1 51520bl1 \([0, -1, 0, -721, -14455]\) \(-40535147776/67648175\) \(-69271731200\) \([]\) \(30720\) \(0.77091\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51520bl1 has rank \(2\).

Complex multiplication

The elliptic curves in class 51520bl do not have complex multiplication.

Modular form 51520.2.a.bl

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} - 2 q^{9} - 2 q^{11} + q^{13} + q^{15} - 2 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display