Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 54390ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54390.bg4 | 54390ba1 | \([1, 0, 1, -69746038, 210822379016]\) | \(318929057401476905525449/21353131537921474560\) | \(2512174572304923560509440\) | \([2]\) | \(14192640\) | \(3.4310\) | \(\Gamma_0(N)\)-optimal |
| 54390.bg2 | 54390ba2 | \([1, 0, 1, -1097350518, 13991409497608]\) | \(1242142983306846366056931529/6179359141291622400\) | \(726995423613818083737600\) | \([2, 2]\) | \(28385280\) | \(3.7776\) | |
| 54390.bg3 | 54390ba3 | \([1, 0, 1, -1078785398, 14487662581256]\) | \(-1180159344892952613848670409/87759036144023189760000\) | \(-10324762843308184252074240000\) | \([2]\) | \(56770560\) | \(4.1241\) | |
| 54390.bg1 | 54390ba4 | \([1, 0, 1, -17557587318, 895456842421768]\) | \(5087799435928552778197163696329/125914832087040\) | \(14813754080208168960\) | \([2]\) | \(56770560\) | \(4.1241\) |
Rank
sage: E.rank()
The elliptic curves in class 54390ba have rank \(0\).
Complex multiplication
The elliptic curves in class 54390ba do not have complex multiplication.Modular form 54390.2.a.ba
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
