Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("53312.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53312f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53312.o1 53312f1 [0, 1, 0, -65, -1793] [] 16128 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 53312.2.a.o

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