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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 24336l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24336.t3 | 24336l1 | \([0, 0, 0, -59826, 5630911]\) | \(420616192/117\) | \(6587088320592\) | \([2]\) | \(86016\) | \(1.4415\) | \(\Gamma_0(N)\)-optimal |
| 24336.t2 | 24336l2 | \([0, 0, 0, -67431, 4108390]\) | \(37642192/13689\) | \(12331029336148224\) | \([2, 2]\) | \(172032\) | \(1.7880\) | |
| 24336.t4 | 24336l3 | \([0, 0, 0, 206349, 29022370]\) | \(269676572/257049\) | \(-926197314581799936\) | \([2]\) | \(344064\) | \(2.1346\) | |
| 24336.t1 | 24336l4 | \([0, 0, 0, -462891, -118246934]\) | \(3044193988/85293\) | \(307327192685540352\) | \([2]\) | \(344064\) | \(2.1346\) |
Rank
sage: E.rank()
The elliptic curves in class 24336l have rank \(0\).
Complex multiplication
The elliptic curves in class 24336l do not have complex multiplication.Modular form 24336.2.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 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.
