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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 51520.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51520.br1 | 51520bo1 | \([0, 1, 0, -10531241, -13157801905]\) | \(-126142795384287538429696/9315359375\) | \(-9538928000000\) | \([]\) | \(1133568\) | \(2.3868\) | \(\Gamma_0(N)\)-optimal |
| 51520.br2 | 51520bo2 | \([0, 1, 0, -10425241, -13435530305]\) | \(-122372013839654770813696/5297595236711512175\) | \(-5424737522392588467200\) | \([]\) | \(3400704\) | \(2.9361\) |
Rank
sage: E.rank()
The elliptic curves in class 51520.br have rank \(1\).
Complex multiplication
The elliptic curves in class 51520.br do not have complex multiplication.Modular form 51520.2.a.br
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
