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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 129437.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129437.c1 | 129437b1 | \([0, -1, 1, -150169, 22448743]\) | \(-78843215872/539\) | \(-2560306185899\) | \([]\) | \(460800\) | \(1.5618\) | \(\Gamma_0(N)\)-optimal |
| 129437.c2 | 129437b2 | \([0, -1, 1, -82929, 42528288]\) | \(-13278380032/156590819\) | \(-743822713433563379\) | \([]\) | \(1382400\) | \(2.1111\) | |
| 129437.c3 | 129437b3 | \([0, -1, 1, 740761, -1100341587]\) | \(9463555063808/115539436859\) | \(-548824369026687619019\) | \([]\) | \(4147200\) | \(2.6604\) |
Rank
sage: E.rank()
The elliptic curves in class 129437.c have rank \(0\).
Complex multiplication
The elliptic curves in class 129437.c do not have complex multiplication.Modular form 129437.2.a.c
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.
