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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 214774.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 214774.e1 | 214774j2 | \([1, -1, 0, -3492662822, 79448898174964]\) | \(2616032722429824267375/129231424\) | \(232765523282253413312\) | \([2]\) | \(66134016\) | \(3.8312\) | |
| 214774.e2 | 214774j1 | \([1, -1, 0, -218279782, 1241569017780]\) | \(-638577663082635375/141954125824\) | \(-255681051533551177920512\) | \([2]\) | \(33067008\) | \(3.4846\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 214774.e have rank \(1\).
Complex multiplication
The elliptic curves in class 214774.e do not have complex multiplication.Modular form 214774.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
