Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 10608k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10608.ba3 | 10608k1 | \([0, 1, 0, -447, -3312]\) | \(618724784128/87947613\) | \(1407161808\) | \([2]\) | \(5120\) | \(0.48121\) | \(\Gamma_0(N)\)-optimal |
| 10608.ba2 | 10608k2 | \([0, 1, 0, -1892, 27900]\) | \(2927363579728/320445801\) | \(82034125056\) | \([2, 2]\) | \(10240\) | \(0.82778\) | |
| 10608.ba1 | 10608k3 | \([0, 1, 0, -29432, 1933668]\) | \(2753580869496292/39328497\) | \(40272380928\) | \([4]\) | \(20480\) | \(1.1744\) | |
| 10608.ba4 | 10608k4 | \([0, 1, 0, 2528, 142820]\) | \(1744147297148/9513325341\) | \(-9741645149184\) | \([2]\) | \(20480\) | \(1.1744\) |
Rank
sage: E.rank()
The elliptic curves in class 10608k have rank \(0\).
Complex multiplication
The elliptic curves in class 10608k do not have complex multiplication.Modular form 10608.2.a.k
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.
