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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 139392ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 139392.bv1 | 139392ct1 | \([0, 0, 0, -3630, -69212]\) | \(16000/3\) | \(991847400192\) | \([2]\) | \(163840\) | \(1.0198\) | \(\Gamma_0(N)\)-optimal |
| 139392.bv2 | 139392ct2 | \([0, 0, 0, 7260, -404624]\) | \(4000/9\) | \(-95217350418432\) | \([2]\) | \(327680\) | \(1.3664\) |
Rank
sage: E.rank()
The elliptic curves in class 139392ct have rank \(1\).
Complex multiplication
The elliptic curves in class 139392ct do not have complex multiplication.Modular form 139392.2.a.ct
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
