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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 200400.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
200400.m1 | 200400bj1 | \([0, -1, 0, -37533, 2811312]\) | \(23390263312384/112725\) | \(28181250000\) | \([2]\) | \(352512\) | \(1.2059\) | \(\Gamma_0(N)\)-optimal |
200400.m2 | 200400bj2 | \([0, -1, 0, -36908, 2908812]\) | \(-1390071129424/101655405\) | \(-406621620000000\) | \([2]\) | \(705024\) | \(1.5525\) |
Rank
sage: E.rank()
The elliptic curves in class 200400.m have rank \(0\).
Complex multiplication
The elliptic curves in class 200400.m do not have complex multiplication.Modular form 200400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.