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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 6069.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6069.d1 | 6069e1 | \([0, 1, 1, 1030189, 364409024]\) | \(5009339741732864/5271114033171\) | \(-127231878682533301299\) | \([]\) | \(156672\) | \(2.5444\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 6069.d1 has rank \(1\).
Complex multiplication
The elliptic curves in class 6069.d do not have complex multiplication.Modular form 6069.2.a.d
sage: E.q_eigenform(10)