Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 22308d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22308.g2 | 22308d1 | \([0, 1, 0, -18477, 39874680]\) | \(-9033613312/8891539371\) | \(-686684196156754224\) | \([2]\) | \(225792\) | \(2.1016\) | \(\Gamma_0(N)\)-optimal |
| 22308.g1 | 22308d2 | \([0, 1, 0, -1866492, 969795828]\) | \(581972233018192/7558011747\) | \(9339156255366482688\) | \([2]\) | \(451584\) | \(2.4481\) |
Rank
sage: E.rank()
The elliptic curves in class 22308d have rank \(1\).
Complex multiplication
The elliptic curves in class 22308d do not have complex multiplication.Modular form 22308.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
