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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 3640.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3640.e1 | 3640c3 | \([0, 0, 0, -1403, -20218]\) | \(298261205316/156065\) | \(159810560\) | \([2]\) | \(1536\) | \(0.52463\) | |
3640.e2 | 3640c4 | \([0, 0, 0, -803, 8622]\) | \(55920415716/999635\) | \(1023626240\) | \([2]\) | \(1536\) | \(0.52463\) | |
3640.e3 | 3640c2 | \([0, 0, 0, -103, -198]\) | \(472058064/207025\) | \(52998400\) | \([2, 2]\) | \(768\) | \(0.17806\) | |
3640.e4 | 3640c1 | \([0, 0, 0, 22, -23]\) | \(73598976/56875\) | \(-910000\) | \([2]\) | \(384\) | \(-0.16852\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3640.e have rank \(0\).
Complex multiplication
The elliptic curves in class 3640.e do not have complex multiplication.Modular form 3640.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.