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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 224400dm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 224400.bc1 | 224400dm1 | \([0, -1, 0, -72808, -53289488]\) | \(-16673509288825/469998676422\) | \(-1203196611640320000\) | \([]\) | \(3297024\) | \(2.1498\) | \(\Gamma_0(N)\)-optimal |
| 224400.bc2 | 224400dm2 | \([0, -1, 0, 653192, 1413811312]\) | \(12039422435197175/344379193347288\) | \(-881610734969057280000\) | \([]\) | \(9891072\) | \(2.6991\) |
Rank
sage: E.rank()
The elliptic curves in class 224400dm have rank \(1\).
Complex multiplication
The elliptic curves in class 224400dm do not have complex multiplication.Modular form 224400.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
