Show commands:
SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 130050.ey
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 130050.ey1 | 130050i4 | \([1, -1, 1, -53842055, -151556907553]\) | \(502270291349/1889568\) | \(64940199897578062500000\) | \([2]\) | \(16384000\) | \(3.2367\) | |
| 130050.ey2 | 130050i2 | \([1, -1, 1, -3447680, 2464558697]\) | \(131872229/18\) | \(618619493003906250\) | \([2]\) | \(3276800\) | \(2.4319\) | |
| 130050.ey3 | 130050i3 | \([1, -1, 1, -1822055, -4548387553]\) | \(-19465109/248832\) | \(-8551795871286000000000\) | \([2]\) | \(8192000\) | \(2.8901\) | |
| 130050.ey4 | 130050i1 | \([1, -1, 1, -196430, 45628697]\) | \(-24389/12\) | \(-412412995335937500\) | \([2]\) | \(1638400\) | \(2.0854\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 130050.ey have rank \(0\).
Complex multiplication
The elliptic curves in class 130050.ey do not have complex multiplication.Modular form 130050.2.a.ey
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.
\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
