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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 3234q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3234.r2 | 3234q1 | \([1, 1, 1, -155772, -26427171]\) | \(-10358806345399/1445216256\) | \(-58319688824635392\) | \([2]\) | \(37632\) | \(1.9485\) | \(\Gamma_0(N)\)-optimal |
| 3234.r1 | 3234q2 | \([1, 1, 1, -2570492, -1587302179]\) | \(46546832455691959/748268928\) | \(30195350250823296\) | \([2]\) | \(75264\) | \(2.2951\) |
Rank
sage: E.rank()
The elliptic curves in class 3234q have rank \(0\).
Complex multiplication
The elliptic curves in class 3234q do not have complex multiplication.Modular form 3234.2.a.q
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.
