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SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 102960.dp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.dp1 | 102960ek4 | \([0, 0, 0, -103107, -12701374]\) | \(40597630665409/154169730\) | \(460348347064320\) | \([2]\) | \(491520\) | \(1.6725\) | |
| 102960.dp2 | 102960ek2 | \([0, 0, 0, -9507, 9506]\) | \(31824875809/18404100\) | \(54954348134400\) | \([2, 2]\) | \(245760\) | \(1.3259\) | |
| 102960.dp3 | 102960ek1 | \([0, 0, 0, -6627, 207074]\) | \(10779215329/34320\) | \(102478970880\) | \([2]\) | \(122880\) | \(0.97937\) | \(\Gamma_0(N)\)-optimal |
| 102960.dp4 | 102960ek3 | \([0, 0, 0, 38013, 76034]\) | \(2034382787711/1178141250\) | \(-3517910922240000\) | \([2]\) | \(491520\) | \(1.6725\) |
Rank
sage: E.rank()
The elliptic curves in class 102960.dp have rank \(1\).
Complex multiplication
The elliptic curves in class 102960.dp do not have complex multiplication.Modular form 102960.2.a.dp
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
