Properties

Label 53312bi
Number of curves $1$
Conductor $53312$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 53312bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53312.v1 53312bi1 \([0, -1, 0, 2287, 43345]\) \(14000/17\) \(-1605658492928\) \([]\) \(64512\) \(1.0282\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53312bi1 has rank \(2\).

Complex multiplication

The elliptic curves in class 53312bi do not have complex multiplication.

Modular form 53312.2.a.bi

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