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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 15246.bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15246.bo1 | 15246bs4 | \([1, -1, 1, -1463639, 681917811]\) | \(268498407453697/252\) | \(325449928188\) | \([2]\) | \(163840\) | \(1.9374\) | |
15246.bo2 | 15246bs5 | \([1, -1, 1, -995369, -378310809]\) | \(84448510979617/933897762\) | \(1206099045943785378\) | \([2]\) | \(327680\) | \(2.2839\) | |
15246.bo3 | 15246bs3 | \([1, -1, 1, -113279, 5221923]\) | \(124475734657/63011844\) | \(81377778193624836\) | \([2, 2]\) | \(163840\) | \(1.9374\) | |
15246.bo4 | 15246bs2 | \([1, -1, 1, -91499, 10666923]\) | \(65597103937/63504\) | \(82013381903376\) | \([2, 2]\) | \(81920\) | \(1.5908\) | |
15246.bo5 | 15246bs1 | \([1, -1, 1, -4379, 247371]\) | \(-7189057/16128\) | \(-20828795404032\) | \([2]\) | \(40960\) | \(1.2442\) | \(\Gamma_0(N)\)-optimal |
15246.bo6 | 15246bs6 | \([1, -1, 1, 420331, 40013295]\) | \(6359387729183/4218578658\) | \(-5448159211514005602\) | \([2]\) | \(327680\) | \(2.2839\) |
Rank
sage: E.rank()
The elliptic curves in class 15246.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 15246.bo do not have complex multiplication.Modular form 15246.2.a.bo
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.