Properties

Label 1296.e
Number of curves $1$
Conductor $1296$
CM no
Rank $1$

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

Elliptic curves in class 1296.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1296.e1 1296c1 \([0, 0, 0, -3, 1]\) \(2304\) \(1296\) \([]\) \(48\) \(-0.70659\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1296.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1296.e do not have complex multiplication.

Modular form 1296.2.a.e

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