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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 35280.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.bs1 | 35280z4 | \([0, 0, 0, -1647723, 814091978]\) | \(5633270409316/14175\) | \(1244912399539200\) | \([2]\) | \(393216\) | \(2.1347\) | |
35280.bs2 | 35280z3 | \([0, 0, 0, -289443, -43871758]\) | \(30534944836/8203125\) | \(720435416400000000\) | \([2]\) | \(393216\) | \(2.1347\) | |
35280.bs3 | 35280z2 | \([0, 0, 0, -104223, 12398078]\) | \(5702413264/275625\) | \(6051657497760000\) | \([2, 2]\) | \(196608\) | \(1.7882\) | |
35280.bs4 | 35280z1 | \([0, 0, 0, 3822, 750827]\) | \(4499456/180075\) | \(-247109347825200\) | \([2]\) | \(98304\) | \(1.4416\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35280.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 35280.bs do not have complex multiplication.Modular form 35280.2.a.bs
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.