Properties

Label 912a
Number of curves $1$
Conductor $912$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 912a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
912.a1 912a1 \([0, -1, 0, -57, -171]\) \(-81415168/13851\) \(-3545856\) \([]\) \(192\) \(-0.016677\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 912a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 912a do not have complex multiplication.

Modular form 912.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} + 3 q^{7} + q^{9} + q^{11} - 2 q^{13} + 3 q^{15} - 5 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display