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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 162240.dm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.dm1 | 162240cx2 | \([0, -1, 0, -2893505, 1328422497]\) | \(4234737878642/1247410125\) | \(789185877513486336000\) | \([2]\) | \(5160960\) | \(2.7156\) | |
| 162240.dm2 | 162240cx1 | \([0, -1, 0, 486495, 137986497]\) | \(40254822716/49359375\) | \(-15613838982144000000\) | \([2]\) | \(2580480\) | \(2.3690\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162240.dm have rank \(1\).
Complex multiplication
The elliptic curves in class 162240.dm do not have complex multiplication.Modular form 162240.2.a.dm
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.
