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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 78400.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78400.dn1 | 78400ht1 | \([0, -1, 0, 1867, 6637]\) | \(8192/5\) | \(-439040000000\) | \([]\) | \(73728\) | \(0.92318\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 78400.dn1 has rank \(1\).
Complex multiplication
The elliptic curves in class 78400.dn do not have complex multiplication.Modular form 78400.2.a.dn
sage: E.q_eigenform(10)