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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 302016q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302016.q4 | 302016q1 | \([0, -1, 0, 3711, -186591]\) | \(12167/39\) | \(-18111759384576\) | \([2]\) | \(655360\) | \(1.2272\) | \(\Gamma_0(N)\)-optimal |
| 302016.q3 | 302016q2 | \([0, -1, 0, -35009, -2161311]\) | \(10218313/1521\) | \(706358615998464\) | \([2, 2]\) | \(1310720\) | \(1.5737\) | |
| 302016.q2 | 302016q3 | \([0, -1, 0, -151169, 20536353]\) | \(822656953/85683\) | \(39791535367913472\) | \([2]\) | \(2621440\) | \(1.9203\) | |
| 302016.q1 | 302016q4 | \([0, -1, 0, -538369, -151860575]\) | \(37159393753/1053\) | \(489017503383552\) | \([2]\) | \(2621440\) | \(1.9203\) |
Rank
sage: E.rank()
The elliptic curves in class 302016q have rank \(2\).
Complex multiplication
The elliptic curves in class 302016q do not have complex multiplication.Modular form 302016.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
