Properties

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

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 1296.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1296.h1 1296a1 \([0, 0, 0, -27, 378]\) \(-36\) \(-60466176\) \([]\) \(288\) \(0.17365\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1296.h1 has rank \(1\).

Complex multiplication

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

Modular form 1296.2.a.h

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