Properties

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

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

Elliptic curves in class 53312.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53312.e1 53312i1 \([0, 0, 0, -97804, 42435568]\) \(-164384733177/1140850688\) \(-718060257774927872\) \([]\) \(1198080\) \(2.1095\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 53312.2.a.e

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