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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 417450j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
417450.j1 | 417450j1 | \([1, 1, 0, -213325, -37377875]\) | \(1551443665/29808\) | \(20627613393750000\) | \([]\) | \(5184000\) | \(1.9235\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 417450j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 417450j do not have complex multiplication.Modular form 417450.2.a.j
sage: E.q_eigenform(10)