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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 34914w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 34914.u4 | 34914w1 | \([1, 1, 1, -1069, -685]\) | \(912673/528\) | \(78162949392\) | \([2]\) | \(49280\) | \(0.77965\) | \(\Gamma_0(N)\)-optimal |
| 34914.u2 | 34914w2 | \([1, 1, 1, -11649, 477531]\) | \(1180932193/4356\) | \(644844332484\) | \([2, 2]\) | \(98560\) | \(1.1262\) | |
| 34914.u3 | 34914w3 | \([1, 1, 1, -6359, 919775]\) | \(-192100033/2371842\) | \(-351117739037538\) | \([2]\) | \(197120\) | \(1.4728\) | |
| 34914.u1 | 34914w4 | \([1, 1, 1, -186219, 30852711]\) | \(4824238966273/66\) | \(9770368674\) | \([2]\) | \(197120\) | \(1.4728\) |
Rank
sage: E.rank()
The elliptic curves in class 34914w have rank \(0\).
Complex multiplication
The elliptic curves in class 34914w do not have complex multiplication.Modular form 34914.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
