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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 110352bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 110352.o3 | 110352bj1 | \([0, -1, 0, -15528, 62064]\) | \(57066625/32832\) | \(238239296520192\) | \([2]\) | \(414720\) | \(1.4483\) | \(\Gamma_0(N)\)-optimal |
| 110352.o4 | 110352bj2 | \([0, -1, 0, 61912, 433776]\) | \(3616805375/2105352\) | \(-15277094889357312\) | \([2]\) | \(829440\) | \(1.7949\) | |
| 110352.o1 | 110352bj3 | \([0, -1, 0, -828648, -290059152]\) | \(8671983378625/82308\) | \(597252680859648\) | \([2]\) | \(1244160\) | \(1.9976\) | |
| 110352.o2 | 110352bj4 | \([0, -1, 0, -809288, -304277136]\) | \(-8078253774625/846825858\) | \(-6144834207024488448\) | \([2]\) | \(2488320\) | \(2.3442\) |
Rank
sage: E.rank()
The elliptic curves in class 110352bj have rank \(2\).
Complex multiplication
The elliptic curves in class 110352bj do not have complex multiplication.Modular form 110352.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
