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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2704g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2704.f3 | 2704g1 | \([0, -1, 0, 1296, -29888]\) | \(12167/26\) | \(-514035851264\) | \([]\) | \(2688\) | \(0.93140\) | \(\Gamma_0(N)\)-optimal |
| 2704.f2 | 2704g2 | \([0, -1, 0, -12224, 1040896]\) | \(-10218313/17576\) | \(-347488235454464\) | \([]\) | \(8064\) | \(1.4807\) | |
| 2704.f1 | 2704g3 | \([0, -1, 0, -1242544, 533523392]\) | \(-10730978619193/6656\) | \(-131593177923584\) | \([]\) | \(24192\) | \(2.0300\) |
Rank
sage: E.rank()
The elliptic curves in class 2704g have rank \(0\).
Complex multiplication
The elliptic curves in class 2704g do not have complex multiplication.Modular form 2704.2.a.g
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
