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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 98192.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98192.l1 | 98192v4 | \([0, 0, 0, -523811, -145918366]\) | \(82483294977/17\) | \(3275898785792\) | \([2]\) | \(442368\) | \(1.7887\) | |
| 98192.l2 | 98192v2 | \([0, 0, 0, -32851, -2263470]\) | \(20346417/289\) | \(55690279358464\) | \([2, 2]\) | \(221184\) | \(1.4422\) | |
| 98192.l3 | 98192v3 | \([0, 0, 0, -3971, -6104510]\) | \(-35937/83521\) | \(-16094490734596096\) | \([2]\) | \(442368\) | \(1.7887\) | |
| 98192.l4 | 98192v1 | \([0, 0, 0, -3971, 41154]\) | \(35937/17\) | \(3275898785792\) | \([2]\) | \(110592\) | \(1.0956\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 98192.l have rank \(2\).
Complex multiplication
The elliptic curves in class 98192.l do not have complex multiplication.Modular form 98192.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
