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SageMath
E = EllipticCurve("bdr1")
E.isogeny_class()
Elliptic curves in class 2116800.bdr
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 2116800.bdr1 | \([0, 0, 0, -83275500, 292498738000]\) | \(-545407363875/14\) | \(-1639390814208000000\) | \([]\) | \(143327232\) | \(3.0113\) |
| 2116800.bdr2 | \([0, 0, 0, -955500, 460306000]\) | \(-7414875/2744\) | \(-35702288842752000000\) | \([]\) | \(47775744\) | \(2.4620\) |
| 2116800.bdr3 | \([0, 0, 0, 7276500, -4649022000]\) | \(4492125/3584\) | \(-33994407923417088000000\) | \([]\) | \(143327232\) | \(3.0113\) |
Rank
sage: E.rank()
The elliptic curves in class 2116800.bdr have rank \(1\).
Complex multiplication
The elliptic curves in class 2116800.bdr do not have complex multiplication.Modular form 2116800.2.a.bdr
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.
