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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 79968.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 79968.i1 | 79968bw4 | \([0, -1, 0, -62344, 6012280]\) | \(444893916104/9639\) | \(580617580032\) | \([2]\) | \(172032\) | \(1.3737\) | |
| 79968.i2 | 79968bw3 | \([0, -1, 0, -16529, -724191]\) | \(1036433728/122451\) | \(59007949615104\) | \([2]\) | \(172032\) | \(1.3737\) | |
| 79968.i3 | 79968bw1 | \([0, -1, 0, -4034, 87984]\) | \(964430272/127449\) | \(959631833664\) | \([2, 2]\) | \(86016\) | \(1.0271\) | \(\Gamma_0(N)\)-optimal |
| 79968.i4 | 79968bw2 | \([0, -1, 0, 6256, 454308]\) | \(449455096/1753941\) | \(-105650895211008\) | \([2]\) | \(172032\) | \(1.3737\) |
Rank
sage: E.rank()
The elliptic curves in class 79968.i have rank \(0\).
Complex multiplication
The elliptic curves in class 79968.i do not have complex multiplication.Modular form 79968.2.a.i
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.
