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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 3520g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3520.bd4 | 3520g1 | \([0, -1, 0, -181, 981]\) | \(643956736/15125\) | \(15488000\) | \([2]\) | \(1152\) | \(0.16514\) | \(\Gamma_0(N)\)-optimal |
| 3520.bd3 | 3520g2 | \([0, -1, 0, -401, -1615]\) | \(436334416/171875\) | \(2816000000\) | \([2]\) | \(2304\) | \(0.51172\) | |
| 3520.bd2 | 3520g3 | \([0, -1, 0, -1781, -27979]\) | \(610462990336/8857805\) | \(9070392320\) | \([2]\) | \(3456\) | \(0.71445\) | |
| 3520.bd1 | 3520g4 | \([0, -1, 0, -28401, -1832815]\) | \(154639330142416/33275\) | \(545177600\) | \([2]\) | \(6912\) | \(1.0610\) |
Rank
sage: E.rank()
The elliptic curves in class 3520g have rank \(0\).
Complex multiplication
The elliptic curves in class 3520g do not have complex multiplication.Modular form 3520.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
