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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 121495.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121495.c1 | 121495c4 | \([1, -1, 0, -130745, -18159050]\) | \(22930509321/6875\) | \(74107105386875\) | \([2]\) | \(397440\) | \(1.6394\) | |
| 121495.c2 | 121495c3 | \([1, -1, 0, -64475, 6170876]\) | \(2749884201/73205\) | \(789092458159445\) | \([2]\) | \(397440\) | \(1.6394\) | |
| 121495.c3 | 121495c2 | \([1, -1, 0, -9250, -202089]\) | \(8120601/3025\) | \(32607126370225\) | \([2, 2]\) | \(198720\) | \(1.2928\) | |
| 121495.c4 | 121495c1 | \([1, -1, 0, 1795, -23160]\) | \(59319/55\) | \(-592856843095\) | \([2]\) | \(99360\) | \(0.94626\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 121495.c have rank \(1\).
Complex multiplication
The elliptic curves in class 121495.c do not have complex multiplication.Modular form 121495.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
