Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("53312.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53312ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53312.t1 53312ca1 [0, -1, 0, -17425, 1249361] [] 258048 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53312ca1 has rank \(2\).

Modular form 53312.2.a.t

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