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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 29435.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29435.c1 | 29435c3 | \([0, -1, 1, -110451, -14743143]\) | \(-250523582464/13671875\) | \(-8132350091796875\) | \([]\) | \(149688\) | \(1.8111\) | |
| 29435.c2 | 29435c1 | \([0, -1, 1, -1121, 16407]\) | \(-262144/35\) | \(-20818816235\) | \([]\) | \(16632\) | \(0.71250\) | \(\Gamma_0(N)\)-optimal |
| 29435.c3 | 29435c2 | \([0, -1, 1, 7289, -43304]\) | \(71991296/42875\) | \(-25503049887875\) | \([]\) | \(49896\) | \(1.2618\) |
Rank
sage: E.rank()
The elliptic curves in class 29435.c have rank \(0\).
Complex multiplication
The elliptic curves in class 29435.c do not have complex multiplication.Modular form 29435.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
