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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 381150.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 381150.m1 | 381150m3 | \([1, -1, 0, -2636224542, 52098663848116]\) | \(100407751863770656369/166028940000\) | \(3350329030265982187500000\) | \([2]\) | \(235929600\) | \(3.9687\) | |
| 381150.m2 | 381150m2 | \([1, -1, 0, -166372542, 797367956116]\) | \(25238585142450289/995844326400\) | \(20095328900874704400000000\) | \([2, 2]\) | \(117964800\) | \(3.6221\) | |
| 381150.m3 | 381150m1 | \([1, -1, 0, -26980542, -37171947884]\) | \(107639597521009/32699842560\) | \(659856238399733760000000\) | \([2]\) | \(58982400\) | \(3.2755\) | \(\Gamma_0(N)\)-optimal |
| 381150.m4 | 381150m4 | \([1, -1, 0, 73207458, 2904953216116]\) | \(2150235484224911/181905111732960\) | \(-3670697268757561274347500000\) | \([2]\) | \(235929600\) | \(3.9687\) |
Rank
sage: E.rank()
The elliptic curves in class 381150.m have rank \(1\).
Complex multiplication
The elliptic curves in class 381150.m do not have complex multiplication.Modular form 381150.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
