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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 29120.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29120.m1 | 29120cc4 | \([0, 1, 0, -938785, 349785183]\) | \(349046010201856969/7245875000\) | \(1899462656000000\) | \([2]\) | \(331776\) | \(2.0504\) | |
29120.m2 | 29120cc3 | \([0, 1, 0, -60705, 5050975]\) | \(94376601570889/12235496000\) | \(3207461863424000\) | \([2]\) | \(165888\) | \(1.7039\) | |
29120.m3 | 29120cc2 | \([0, 1, 0, -19425, -253025]\) | \(3092354182009/1689383150\) | \(442861656473600\) | \([2]\) | \(110592\) | \(1.5011\) | |
29120.m4 | 29120cc1 | \([0, 1, 0, -14945, -707297]\) | \(1408317602329/2153060\) | \(564411760640\) | \([2]\) | \(55296\) | \(1.1546\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29120.m have rank \(1\).
Complex multiplication
The elliptic curves in class 29120.m do not have complex multiplication.Modular form 29120.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.