Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 137904.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 137904.bw1 | 137904cd3 | \([0, 1, 0, -4974064, 4268164772]\) | \(2753580869496292/39328497\) | \(194387090714698752\) | \([2]\) | \(3440640\) | \(2.4568\) | |
| 137904.bw2 | 137904cd2 | \([0, 1, 0, -319804, 62575436]\) | \(2927363579728/320445801\) | \(395963053127426304\) | \([2, 2]\) | \(1720320\) | \(2.1103\) | |
| 137904.bw3 | 137904cd1 | \([0, 1, 0, -75599, -6974148]\) | \(618724784128/87947613\) | \(6792101279310672\) | \([2]\) | \(860160\) | \(1.7637\) | \(\Gamma_0(N)\)-optimal |
| 137904.bw4 | 137904cd4 | \([0, 1, 0, 427176, 312066756]\) | \(1744147297148/9513325341\) | \(-47021060480887673856\) | \([4]\) | \(3440640\) | \(2.4568\) |
Rank
sage: E.rank()
The elliptic curves in class 137904.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 137904.bw do not have complex multiplication.Modular form 137904.2.a.bw
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.
