Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 3330.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3330.k1 | 3330b2 | \([1, -1, 0, -3686379, 2725178885]\) | \(281470209323873024547/35046400\) | \(689818291200\) | \([2]\) | \(84480\) | \(2.1331\) | |
| 3330.k2 | 3330b1 | \([1, -1, 0, -230379, 42631685]\) | \(-68700855708416547/24248320000\) | \(-477279682560000\) | \([2]\) | \(42240\) | \(1.7865\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3330.k have rank \(0\).
Complex multiplication
The elliptic curves in class 3330.k do not have complex multiplication.Modular form 3330.2.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 LMFDB 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 LMFDB labels.
