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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 76440j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76440.m2 | 76440j1 | \([0, -1, 0, -21996, -1248204]\) | \(13404187799728/1584375\) | \(139120800000\) | \([2]\) | \(153600\) | \(1.1638\) | \(\Gamma_0(N)\)-optimal |
| 76440.m1 | 76440j2 | \([0, -1, 0, -23816, -1027620]\) | \(4253577358972/1142578125\) | \(401310000000000\) | \([2]\) | \(307200\) | \(1.5103\) |
Rank
sage: E.rank()
The elliptic curves in class 76440j have rank \(1\).
Complex multiplication
The elliptic curves in class 76440j do not have complex multiplication.Modular form 76440.2.a.j
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
