Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2394g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2394.k4 | 2394g1 | \([1, -1, 1, -485, 4061]\) | \(466385893875/21509824\) | \(580765248\) | \([6]\) | \(1152\) | \(0.44316\) | \(\Gamma_0(N)\)-optimal |
| 2394.k3 | 2394g2 | \([1, -1, 1, -1325, -13075]\) | \(9521387989875/2634569336\) | \(71133372072\) | \([6]\) | \(2304\) | \(0.78973\) | |
| 2394.k2 | 2394g3 | \([1, -1, 1, -6185, -184571]\) | \(1329185824875/8941324\) | \(175992080292\) | \([2]\) | \(3456\) | \(0.99246\) | |
| 2394.k1 | 2394g4 | \([1, -1, 1, -98795, -11927519]\) | \(5417927574172875/247646\) | \(4874416218\) | \([2]\) | \(6912\) | \(1.3390\) |
Rank
sage: E.rank()
The elliptic curves in class 2394g have rank \(0\).
Complex multiplication
The elliptic curves in class 2394g do not have complex multiplication.Modular form 2394.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
