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SageMath
E = EllipticCurve("lh1")
E.isogeny_class()
Elliptic curves in class 78400.lh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78400.lh1 | 78400p1 | \([0, 0, 0, -10324300, 12768518000]\) | \(-5154200289/20\) | \(-472252497920000000\) | \([]\) | \(3870720\) | \(2.6046\) | \(\Gamma_0(N)\)-optimal |
| 78400.lh2 | 78400p2 | \([0, 0, 0, 71995700, -121149658000]\) | \(1747829720511/1280000000\) | \(-30224159866880000000000000\) | \([]\) | \(27095040\) | \(3.5775\) |
Rank
sage: E.rank()
The elliptic curves in class 78400.lh have rank \(1\).
Complex multiplication
The elliptic curves in class 78400.lh do not have complex multiplication.Modular form 78400.2.a.lh
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
