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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 215600m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 215600.n2 | 215600m1 | \([0, 1, 0, -1535333, 723186463]\) | \(34020720640/456533\) | \(5371065091700000000\) | \([]\) | \(3732480\) | \(2.4008\) | \(\Gamma_0(N)\)-optimal |
| 215600.n1 | 215600m2 | \([0, 1, 0, -12315333, -16271483537]\) | \(17557957181440/443889677\) | \(5222317660937300000000\) | \([]\) | \(11197440\) | \(2.9501\) |
Rank
sage: E.rank()
The elliptic curves in class 215600m have rank \(0\).
Complex multiplication
The elliptic curves in class 215600m do not have complex multiplication.Modular form 215600.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
