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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 56784o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56784.cz1 | 56784o1 | \([0, 1, 0, -54126024, 171491539428]\) | \(-20994006260678308/3063651608241\) | \(-2559093488930038243083264\) | \([]\) | \(11980800\) | \(3.4138\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 56784o1 has rank \(0\).
Complex multiplication
The elliptic curves in class 56784o do not have complex multiplication.Modular form 56784.2.a.o
sage: E.q_eigenform(10)