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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 36414.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 36414.l1 | 36414bh4 | \([1, -1, 0, -13210533, -18477825219]\) | \(14489843500598257/6246072\) | \(109907680537767672\) | \([2]\) | \(1769472\) | \(2.6125\) | |
| 36414.l2 | 36414bh3 | \([1, -1, 0, -1766133, 477971469]\) | \(34623662831857/14438442312\) | \(254062986320087835912\) | \([2]\) | \(1769472\) | \(2.6125\) | |
| 36414.l3 | 36414bh2 | \([1, -1, 0, -829773, -285536475]\) | \(3590714269297/73410624\) | \(1291754467554997824\) | \([2, 2]\) | \(884736\) | \(2.2659\) | |
| 36414.l4 | 36414bh1 | \([1, -1, 0, 2547, -13367835]\) | \(103823/4386816\) | \(-77191676866031616\) | \([2]\) | \(442368\) | \(1.9193\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 36414.l have rank \(1\).
Complex multiplication
The elliptic curves in class 36414.l do not have complex multiplication.Modular form 36414.2.a.l
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.
