Properties

Label 296a
Number of curves $1$
Conductor $296$
CM no
Rank $1$

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

Elliptic curves in class 296a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
296.a1 296a1 \([0, -1, 0, -9, 13]\) \(351232/37\) \(9472\) \([]\) \(16\) \(-0.50224\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 296a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 296a do not have complex multiplication.

Modular form 296.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + q^{7} - 2 q^{9} + q^{11} - 6 q^{13} + 2 q^{15} - 4 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display