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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 317520bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 317520.bm2 | 317520bm1 | \([0, 0, 0, -1323, -574182]\) | \(-9/5\) | \(-142275702804480\) | \([]\) | \(760320\) | \(1.3948\) | \(\Gamma_0(N)\)-optimal |
| 317520.bm1 | 317520bm2 | \([0, 0, 0, -1588923, 774238122]\) | \(-15590912409/78125\) | \(-2223057856320000000\) | \([]\) | \(5322240\) | \(2.3678\) |
Rank
sage: E.rank()
The elliptic curves in class 317520bm have rank \(0\).
Complex multiplication
The elliptic curves in class 317520bm do not have complex multiplication.Modular form 317520.2.a.bm
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
