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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 243360.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 243360.bj1 | 243360bj2 | \([0, 0, 0, -1583868, 767227552]\) | \(30488290624/195\) | \(2810491016785920\) | \([2]\) | \(2064384\) | \(2.1490\) | |
| 243360.bj2 | 243360bj4 | \([0, 0, 0, -329043, -59086118]\) | \(2186875592/428415\) | \(771831095484833280\) | \([2]\) | \(2064384\) | \(2.1490\) | |
| 243360.bj3 | 243360bj1 | \([0, 0, 0, -100893, 11503492]\) | \(504358336/38025\) | \(8563214816769600\) | \([2, 2]\) | \(1032192\) | \(1.8024\) | \(\Gamma_0(N)\)-optimal |
| 243360.bj4 | 243360bj3 | \([0, 0, 0, 96837, 51089038]\) | \(55742968/658125\) | \(-1185675897706560000\) | \([2]\) | \(2064384\) | \(2.1490\) |
Rank
sage: E.rank()
The elliptic curves in class 243360.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 243360.bj do not have complex multiplication.Modular form 243360.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
