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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 121296v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121296.n4 | 121296v1 | \([0, -1, 0, -1573719, -297108522]\) | \(572616640141312/280535480757\) | \(211168621503545790672\) | \([2]\) | \(4423680\) | \(2.5932\) | \(\Gamma_0(N)\)-optimal |
| 121296.n2 | 121296v2 | \([0, -1, 0, -13416324, 18712641024]\) | \(22174957026242512/278654127129\) | \(3356039399697870246144\) | \([2, 2]\) | \(8847360\) | \(2.9398\) | |
| 121296.n3 | 121296v3 | \([0, -1, 0, -2304744, 48758353344]\) | \(-28104147578308/21301741002339\) | \(-1026210992423793987234816\) | \([4]\) | \(17694720\) | \(3.2864\) | |
| 121296.n1 | 121296v4 | \([0, -1, 0, -214009584, 1205101417968]\) | \(22501000029889239268/3620708343\) | \(174427559772656827392\) | \([2]\) | \(17694720\) | \(3.2864\) |
Rank
sage: E.rank()
The elliptic curves in class 121296v have rank \(1\).
Complex multiplication
The elliptic curves in class 121296v do not have complex multiplication.Modular form 121296.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
