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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 28560de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28560.cl4 | 28560de1 | \([0, 1, 0, -2896, 135380]\) | \(-656008386769/1581036975\) | \(-6475927449600\) | \([2]\) | \(49152\) | \(1.1464\) | \(\Gamma_0(N)\)-optimal |
| 28560.cl3 | 28560de2 | \([0, 1, 0, -61216, 5804084]\) | \(6193921595708449/6452105625\) | \(26427824640000\) | \([2, 2]\) | \(98304\) | \(1.4930\) | |
| 28560.cl2 | 28560de3 | \([0, 1, 0, -76336, 2701460]\) | \(12010404962647729/6166198828125\) | \(25256750400000000\) | \([2]\) | \(196608\) | \(1.8395\) | |
| 28560.cl1 | 28560de4 | \([0, 1, 0, -979216, 372636884]\) | \(25351269426118370449/27551475\) | \(112850841600\) | \([2]\) | \(196608\) | \(1.8395\) |
Rank
sage: E.rank()
The elliptic curves in class 28560de have rank \(1\).
Complex multiplication
The elliptic curves in class 28560de do not have complex multiplication.Modular form 28560.2.a.de
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.
