Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 35321a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35321.c1 | 35321a1 | \([0, 1, 1, -4619, 139780]\) | \(-2258403328/480491\) | \(-2319238283219\) | \([]\) | \(55296\) | \(1.0941\) | \(\Gamma_0(N)\)-optimal |
| 35321.c2 | 35321a2 | \([0, 1, 1, 32561, -806451]\) | \(790939860992/517504691\) | \(-2497896300061019\) | \([]\) | \(165888\) | \(1.6434\) |
Rank
sage: E.rank()
The elliptic curves in class 35321a have rank \(1\).
Complex multiplication
The elliptic curves in class 35321a do not have complex multiplication.Modular form 35321.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
