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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 79560.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 79560.bj1 | 79560bo4 | \([0, 0, 0, -294267, 61440694]\) | \(1887517194957938/21849165\) | \(32620628551680\) | \([2]\) | \(393216\) | \(1.7442\) | |
| 79560.bj2 | 79560bo2 | \([0, 0, 0, -18867, 907774]\) | \(994958062276/98903025\) | \(73830712550400\) | \([2, 2]\) | \(196608\) | \(1.3976\) | |
| 79560.bj3 | 79560bo1 | \([0, 0, 0, -4287, -92414]\) | \(46689225424/7249905\) | \(1353006270720\) | \([2]\) | \(98304\) | \(1.0510\) | \(\Gamma_0(N)\)-optimal |
| 79560.bj4 | 79560bo3 | \([0, 0, 0, 23253, 4386886]\) | \(931329171502/6107473125\) | \(-9118408515840000\) | \([2]\) | \(393216\) | \(1.7442\) |
Rank
sage: E.rank()
The elliptic curves in class 79560.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 79560.bj do not have complex multiplication.Modular form 79560.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
