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SageMath
E = EllipticCurve("ja1")
E.isogeny_class()
Elliptic curves in class 84672ja
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84672.fw2 | 84672ja1 | \([0, 0, 0, -38220, 3682448]\) | \(-7414875/2744\) | \(-2284946485936128\) | \([]\) | \(331776\) | \(1.6573\) | \(\Gamma_0(N)\)-optimal |
| 84672.fw3 | 84672ja2 | \([0, 0, 0, 291060, -37192176]\) | \(4492125/3584\) | \(-2175642107098693632\) | \([]\) | \(995328\) | \(2.2066\) | |
| 84672.fw1 | 84672ja3 | \([0, 0, 0, -3331020, 2339989904]\) | \(-545407363875/14\) | \(-104921012109312\) | \([]\) | \(995328\) | \(2.2066\) |
Rank
sage: E.rank()
The elliptic curves in class 84672ja have rank \(0\).
Complex multiplication
The elliptic curves in class 84672ja do not have complex multiplication.Modular form 84672.2.a.ja
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.
\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
