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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 12096.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12096.br1 | 12096bg3 | \([0, 0, 0, -67980, 6822128]\) | \(-545407363875/14\) | \(-891813888\) | \([]\) | \(20736\) | \(1.2336\) | |
12096.br2 | 12096bg1 | \([0, 0, 0, -780, 10736]\) | \(-7414875/2744\) | \(-19421724672\) | \([]\) | \(6912\) | \(0.68430\) | \(\Gamma_0(N)\)-optimal |
12096.br3 | 12096bg2 | \([0, 0, 0, 5940, -108432]\) | \(4492125/3584\) | \(-18492652781568\) | \([]\) | \(20736\) | \(1.2336\) |
Rank
sage: E.rank()
The elliptic curves in class 12096.br have rank \(1\).
Complex multiplication
The elliptic curves in class 12096.br do not have complex multiplication.Modular form 12096.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.