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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 10320.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10320.w1 | 10320bb3 | \([0, 1, 0, -11016, -448716]\) | \(36097320816649/80625\) | \(330240000\) | \([2]\) | \(11264\) | \(0.87979\) | |
| 10320.w2 | 10320bb4 | \([0, 1, 0, -1896, 22260]\) | \(184122897769/51282015\) | \(210051133440\) | \([2]\) | \(11264\) | \(0.87979\) | |
| 10320.w3 | 10320bb2 | \([0, 1, 0, -696, -7020]\) | \(9116230969/416025\) | \(1704038400\) | \([2, 2]\) | \(5632\) | \(0.53322\) | |
| 10320.w4 | 10320bb1 | \([0, 1, 0, 24, -396]\) | \(357911/17415\) | \(-71331840\) | \([2]\) | \(2816\) | \(0.18664\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10320.w have rank \(1\).
Complex multiplication
The elliptic curves in class 10320.w do not have complex multiplication.Modular form 10320.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
