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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 92400.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.e1 | 92400g4 | \([0, -1, 0, -206008, -35919488]\) | \(60430765429444/2525985\) | \(40415760000000\) | \([2]\) | \(589824\) | \(1.6915\) | |
| 92400.e2 | 92400g3 | \([0, -1, 0, -63008, 5638512]\) | \(1729010797924/148561875\) | \(2376990000000000\) | \([2]\) | \(589824\) | \(1.6915\) | |
| 92400.e3 | 92400g2 | \([0, -1, 0, -13508, -499488]\) | \(68150496976/12006225\) | \(48024900000000\) | \([2, 2]\) | \(294912\) | \(1.3449\) | |
| 92400.e4 | 92400g1 | \([0, -1, 0, 1617, -45738]\) | \(1869154304/4611915\) | \(-1152978750000\) | \([2]\) | \(147456\) | \(0.99831\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.e have rank \(1\).
Complex multiplication
The elliptic curves in class 92400.e do not have complex multiplication.Modular form 92400.2.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.
