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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 83790.cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83790.cl1 | 83790ck4 | \([1, -1, 0, -1340649, 597811675]\) | \(3107086841064961/570\) | \(48886688970\) | \([2]\) | \(884736\) | \(1.8868\) | |
| 83790.cl2 | 83790ck3 | \([1, -1, 0, -97029, 6213703]\) | \(1177918188481/488703750\) | \(41914224955653750\) | \([2]\) | \(884736\) | \(1.8868\) | |
| 83790.cl3 | 83790ck2 | \([1, -1, 0, -83799, 9354505]\) | \(758800078561/324900\) | \(27865412712900\) | \([2, 2]\) | \(442368\) | \(1.5402\) | |
| 83790.cl4 | 83790ck1 | \([1, -1, 0, -4419, 194053]\) | \(-111284641/123120\) | \(-10559524817520\) | \([2]\) | \(221184\) | \(1.1936\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 83790.cl have rank \(1\).
Complex multiplication
The elliptic curves in class 83790.cl do not have complex multiplication.Modular form 83790.2.a.cl
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.
