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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 13104bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13104.cg2 | 13104bx1 | \([0, 0, 0, -1056, 13232]\) | \(-43614208/91\) | \(-271724544\) | \([]\) | \(6912\) | \(0.50395\) | \(\Gamma_0(N)\)-optimal |
| 13104.cg3 | 13104bx2 | \([0, 0, 0, 1824, 65648]\) | \(224755712/753571\) | \(-2250150948864\) | \([]\) | \(20736\) | \(1.0533\) | |
| 13104.cg1 | 13104bx3 | \([0, 0, 0, -16896, -2083408]\) | \(-178643795968/524596891\) | \(-1566437922975744\) | \([]\) | \(62208\) | \(1.6026\) |
Rank
sage: E.rank()
The elliptic curves in class 13104bx have rank \(0\).
Complex multiplication
The elliptic curves in class 13104bx do not have complex multiplication.Modular form 13104.2.a.bx
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 Cremona 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 Cremona labels.
