Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 48050v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48050.u3 | 48050v1 | \([1, 0, 0, -2903, -72823]\) | \(-121945/32\) | \(-710002944800\) | \([]\) | \(61200\) | \(0.99089\) | \(\Gamma_0(N)\)-optimal |
48050.u4 | 48050v2 | \([1, 0, 0, 21122, 537412]\) | \(46969655/32768\) | \(-727043015475200\) | \([]\) | \(183600\) | \(1.5402\) | |
48050.u2 | 48050v3 | \([1, 0, 0, -12513, 6356267]\) | \(-25/2\) | \(-17334056269531250\) | \([]\) | \(306000\) | \(1.7956\) | |
48050.u1 | 48050v4 | \([1, 0, 0, -3015638, 2015446892]\) | \(-349938025/8\) | \(-69336225078125000\) | \([]\) | \(918000\) | \(2.3449\) |
Rank
sage: E.rank()
The elliptic curves in class 48050v have rank \(1\).
Complex multiplication
The elliptic curves in class 48050v do not have complex multiplication.Modular form 48050.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.