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SageMath
E = EllipticCurve("fq1")
E.isogeny_class()
Elliptic curves in class 84672.fq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84672.fq1 | 84672fv3 | \([0, 0, 0, -29979180, -63179727408]\) | \(-545407363875/14\) | \(-76487417827688448\) | \([]\) | \(2985984\) | \(2.7559\) | |
| 84672.fq2 | 84672fv2 | \([0, 0, 0, -343980, -99426096]\) | \(-7414875/2744\) | \(-1665725988247437312\) | \([]\) | \(995328\) | \(2.2066\) | |
| 84672.fq3 | 84672fv1 | \([0, 0, 0, 32340, 1377488]\) | \(4492125/3584\) | \(-2984419899998208\) | \([]\) | \(331776\) | \(1.6573\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 84672.fq have rank \(1\).
Complex multiplication
The elliptic curves in class 84672.fq do not have complex multiplication.Modular form 84672.2.a.fq
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
