Properties

Label 53312.e
Number of curves $1$
Conductor $53312$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("53312.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53312.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53312.e1 53312i1 [0, 0, 0, -97804, 42435568] [] 1198080 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53312.e1 has rank \(1\).

Modular form 53312.2.a.e

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