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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 101430e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101430.t2 | 101430e1 | \([1, -1, 0, -450, 3296]\) | \(3176523/460\) | \(1461200580\) | \([2]\) | \(55296\) | \(0.48381\) | \(\Gamma_0(N)\)-optimal |
| 101430.t1 | 101430e2 | \([1, -1, 0, -1920, -28750]\) | \(246491883/26450\) | \(84019033350\) | \([2]\) | \(110592\) | \(0.83038\) |
Rank
sage: E.rank()
The elliptic curves in class 101430e have rank \(1\).
Complex multiplication
The elliptic curves in class 101430e do not have complex multiplication.Modular form 101430.2.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 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.
