Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("53312.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53312bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53312.f1 53312bg1 [0, 0, 0, -67228, 6722800] [] 516096 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53312bg1 has rank \(1\).

Modular form 53312.2.a.f

sage: E.q_eigenform(10)
 
\( q - 3q^{3} + 4q^{5} + 6q^{9} - q^{11} + 3q^{13} - 12q^{15} + q^{17} - 2q^{19} + O(q^{20}) \)