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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4235.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4235.c1 | 4235b3 | \([0, 1, 1, -15891, 801301]\) | \(-250523582464/13671875\) | \(-24220560546875\) | \([]\) | \(8100\) | \(1.3264\) | |
| 4235.c2 | 4235b1 | \([0, 1, 1, -161, -929]\) | \(-262144/35\) | \(-62004635\) | \([]\) | \(900\) | \(0.22780\) | \(\Gamma_0(N)\)-optimal |
| 4235.c3 | 4235b2 | \([0, 1, 1, 1049, 2580]\) | \(71991296/42875\) | \(-75955677875\) | \([]\) | \(2700\) | \(0.77710\) |
Rank
sage: E.rank()
The elliptic curves in class 4235.c have rank \(0\).
Complex multiplication
The elliptic curves in class 4235.c do not have complex multiplication.Modular form 4235.2.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.
