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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 19600.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19600.br1 | 19600ci3 | \([0, -1, 0, -2574133, -1662031363]\) | \(-250523582464/13671875\) | \(-102942875000000000000\) | \([]\) | \(497664\) | \(2.5983\) | |
| 19600.br2 | 19600ci1 | \([0, -1, 0, -26133, 1812637]\) | \(-262144/35\) | \(-263533760000000\) | \([]\) | \(55296\) | \(1.4997\) | \(\Gamma_0(N)\)-optimal |
| 19600.br3 | 19600ci2 | \([0, -1, 0, 169867, -4655363]\) | \(71991296/42875\) | \(-322828856000000000\) | \([]\) | \(165888\) | \(2.0490\) |
Rank
sage: E.rank()
The elliptic curves in class 19600.br have rank \(1\).
Complex multiplication
The elliptic curves in class 19600.br do not have complex multiplication.Modular form 19600.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
