Properties

Label 53312bb
Number of curves $1$
Conductor $53312$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 53312bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53312.j1 53312bb1 \([0, 1, 0, -3201, -608609]\) \(-392/17\) \(-157354532306944\) \([]\) \(112896\) \(1.4042\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53312bb1 has rank \(1\).

Complex multiplication

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

Modular form 53312.2.a.bb

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