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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 76230.cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76230.cl1 | 76230cj4 | \([1, -1, 0, -28361394, 58137938568]\) | \(1953542217204454969/170843779260\) | \(220639268617196522940\) | \([2]\) | \(4915200\) | \(2.9449\) | |
| 76230.cl2 | 76230cj3 | \([1, -1, 0, -10283994, -12042317952]\) | \(93137706732176569/5369647977540\) | \(6934728367798541416260\) | \([2]\) | \(4915200\) | \(2.9449\) | |
| 76230.cl3 | 76230cj2 | \([1, -1, 0, -1898694, 772097508]\) | \(586145095611769/140040608400\) | \(180857960107872339600\) | \([2, 2]\) | \(2457600\) | \(2.5983\) | |
| 76230.cl4 | 76230cj1 | \([1, -1, 0, 279306, 75573108]\) | \(1865864036231/2993760000\) | \(-3866345146873440000\) | \([2]\) | \(1228800\) | \(2.2517\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76230.cl have rank \(1\).
Complex multiplication
The elliptic curves in class 76230.cl do not have complex multiplication.Modular form 76230.2.a.cl
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.
