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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 143055.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 143055.m1 | 143055f4 | \([1, -1, 1, -153947, -23204456]\) | \(22930509321/6875\) | \(120974478631875\) | \([2]\) | \(589824\) | \(1.6802\) | |
| 143055.m2 | 143055f3 | \([1, -1, 1, -75917, 7882696]\) | \(2749884201/73205\) | \(1288136248472205\) | \([2]\) | \(589824\) | \(1.6802\) | |
| 143055.m3 | 143055f2 | \([1, -1, 1, -10892, -258434]\) | \(8120601/3025\) | \(53228770598025\) | \([2, 2]\) | \(294912\) | \(1.3337\) | |
| 143055.m4 | 143055f1 | \([1, -1, 1, 2113, -29546]\) | \(59319/55\) | \(-967795829055\) | \([2]\) | \(147456\) | \(0.98710\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 143055.m have rank \(1\).
Complex multiplication
The elliptic curves in class 143055.m do not have complex multiplication.Modular form 143055.2.a.m
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.
