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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 24400z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24400.w2 | 24400z1 | \([0, -1, 0, -2733208, 1734684912]\) | \(282261687531173/1023410176\) | \(8187281408000000000\) | \([2]\) | \(783360\) | \(2.4900\) | \(\Gamma_0(N)\)-optimal |
| 24400.w1 | 24400z2 | \([0, -1, 0, -43693208, 111179804912]\) | \(1153122726940210853/15241216\) | \(121929728000000000\) | \([2]\) | \(1566720\) | \(2.8366\) |
Rank
sage: E.rank()
The elliptic curves in class 24400z have rank \(1\).
Complex multiplication
The elliptic curves in class 24400z do not have complex multiplication.Modular form 24400.2.a.z
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.
