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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 63580.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63580.m1 | 63580d4 | \([0, -1, 0, -2051996, -1130707480]\) | \(154639330142416/33275\) | \(205613467769600\) | \([2]\) | \(1119744\) | \(2.1311\) | |
| 63580.m2 | 63580d3 | \([0, -1, 0, -128701, -17504334]\) | \(610462990336/8857805\) | \(3420894070016720\) | \([2]\) | \(559872\) | \(1.7845\) | |
| 63580.m3 | 63580d2 | \([0, -1, 0, -28996, -1064280]\) | \(436334416/171875\) | \(1062053036000000\) | \([2]\) | \(373248\) | \(1.5818\) | |
| 63580.m4 | 63580d1 | \([0, -1, 0, -13101, 569726]\) | \(643956736/15125\) | \(5841291698000\) | \([2]\) | \(186624\) | \(1.2352\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 63580.m have rank \(1\).
Complex multiplication
The elliptic curves in class 63580.m do not have complex multiplication.Modular form 63580.2.a.m
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.
