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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 172480dm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 172480.ha2 | 172480dm1 | \([0, -1, 0, -51760, 4338342]\) | \(2036792051776/107421875\) | \(808836875000000\) | \([2]\) | \(737280\) | \(1.6175\) | \(\Gamma_0(N)\)-optimal |
| 172480.ha1 | 172480dm2 | \([0, -1, 0, -817385, 284710217]\) | \(125330290485184/378125\) | \(182214771200000\) | \([2]\) | \(1474560\) | \(1.9641\) |
Rank
sage: E.rank()
The elliptic curves in class 172480dm have rank \(0\).
Complex multiplication
The elliptic curves in class 172480dm do not have complex multiplication.Modular form 172480.2.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 Cremona 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 Cremona labels.
