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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 306.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 306.c1 | 306a3 | \([1, -1, 1, -6755, 163235]\) | \(46753267515625/11591221248\) | \(8450000289792\) | \([6]\) | \(576\) | \(1.1907\) | |
| 306.c2 | 306a1 | \([1, -1, 1, -2300, -41857]\) | \(1845026709625/793152\) | \(578207808\) | \([2]\) | \(192\) | \(0.64143\) | \(\Gamma_0(N)\)-optimal |
| 306.c3 | 306a2 | \([1, -1, 1, -1940, -55681]\) | \(-1107111813625/1228691592\) | \(-895716170568\) | \([2]\) | \(384\) | \(0.98800\) | |
| 306.c4 | 306a4 | \([1, -1, 1, 16285, 1020323]\) | \(655215969476375/1001033261568\) | \(-729753247683072\) | \([6]\) | \(1152\) | \(1.5373\) |
Rank
sage: E.rank()
The elliptic curves in class 306.c have rank \(0\).
Complex multiplication
The elliptic curves in class 306.c do not have complex multiplication.Modular form 306.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
