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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 299832.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
299832.m1 | 299832m3 | \([0, 1, 0, -292464, 59288112]\) | \(3044193988/85293\) | \(77514599898657792\) | \([2]\) | \(3870720\) | \(2.0198\) | |
299832.m2 | 299832m2 | \([0, 1, 0, -42604, -2077504]\) | \(37642192/13689\) | \(3110153699637504\) | \([2, 2]\) | \(1935360\) | \(1.6733\) | |
299832.m3 | 299832m1 | \([0, 1, 0, -37799, -2840538]\) | \(420616192/117\) | \(1661406890832\) | \([2]\) | \(967680\) | \(1.3267\) | \(\Gamma_0(N)\)-optimal |
299832.m4 | 299832m4 | \([0, 1, 0, 130376, -14532064]\) | \(269676572/257049\) | \(-233607100106105856\) | \([2]\) | \(3870720\) | \(2.0198\) |
Rank
sage: E.rank()
The elliptic curves in class 299832.m have rank \(1\).
Complex multiplication
The elliptic curves in class 299832.m do not have complex multiplication.Modular form 299832.2.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.