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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 36784x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36784.c1 | 36784x1 | \([0, 0, 0, -715, 7546]\) | \(-81563625/2432\) | \(-1205338112\) | \([]\) | \(36288\) | \(0.52076\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 36784x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 36784x do not have complex multiplication.Modular form 36784.2.a.x
sage: E.q_eigenform(10)