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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 254320.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254320.e1 | 254320e4 | \([0, 1, 0, -2051996, 1130707480]\) | \(154639330142416/33275\) | \(205613467769600\) | \([2]\) | \(4478976\) | \(2.1311\) | |
| 254320.e2 | 254320e3 | \([0, 1, 0, -128701, 17504334]\) | \(610462990336/8857805\) | \(3420894070016720\) | \([2]\) | \(2239488\) | \(1.7845\) | |
| 254320.e3 | 254320e2 | \([0, 1, 0, -28996, 1064280]\) | \(436334416/171875\) | \(1062053036000000\) | \([2]\) | \(1492992\) | \(1.5818\) | |
| 254320.e4 | 254320e1 | \([0, 1, 0, -13101, -569726]\) | \(643956736/15125\) | \(5841291698000\) | \([2]\) | \(746496\) | \(1.2352\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254320.e have rank \(0\).
Complex multiplication
The elliptic curves in class 254320.e do not have complex multiplication.Modular form 254320.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
