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SageMath
E = EllipticCurve("gd1")
E.isogeny_class()
Elliptic curves in class 405600gd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 405600.gd1 | 405600gd1 | \([0, 1, 0, -140833, -8918239537]\) | \(-1600/177957\) | \(-34358577968520000000000\) | \([]\) | \(38707200\) | \(3.0032\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 405600gd1 has rank \(0\).
Complex multiplication
The elliptic curves in class 405600gd do not have complex multiplication.Modular form 405600.2.a.gd
sage: E.q_eigenform(10)