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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 14400.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14400.m1 | 14400eg4 | \([0, 0, 0, -432300, 109402000]\) | \(23937672968/45\) | \(16796160000000\) | \([2]\) | \(98304\) | \(1.7929\) | |
14400.m2 | 14400eg3 | \([0, 0, 0, -72300, -5258000]\) | \(111980168/32805\) | \(12244400640000000\) | \([2]\) | \(98304\) | \(1.7929\) | |
14400.m3 | 14400eg2 | \([0, 0, 0, -27300, 1672000]\) | \(48228544/2025\) | \(94478400000000\) | \([2, 2]\) | \(49152\) | \(1.4463\) | |
14400.m4 | 14400eg1 | \([0, 0, 0, 825, 97000]\) | \(85184/5625\) | \(-4100625000000\) | \([2]\) | \(24576\) | \(1.0998\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14400.m have rank \(1\).
Complex multiplication
The elliptic curves in class 14400.m do not have complex multiplication.Modular form 14400.2.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.