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SageMath
E = EllipticCurve("er1")
E.isogeny_class()
Elliptic curves in class 289728.er
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
289728.er1 | 289728er1 | \([0, 0, 0, -468, 4320]\) | \(-3796416/503\) | \(-1501949952\) | \([]\) | \(261632\) | \(0.49360\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 289728.er1 has rank \(0\).
Complex multiplication
The elliptic curves in class 289728.er do not have complex multiplication.Modular form 289728.2.a.er
sage: E.q_eigenform(10)