Properties

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

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

Elliptic curves in class 53312f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53312.o1 53312f1 \([0, 1, 0, -65, -1793]\) \(-392/17\) \(-1337491456\) \([]\) \(16128\) \(0.43125\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53312f1 has rank \(1\).

Complex multiplication

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

Modular form 53312.2.a.f

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