Show commands:
SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 366912dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 366912.dn2 | 366912dn1 | \([0, 0, 0, -275331, -89776820]\) | \(-420526439488/390971529\) | \(-2146055133681216576\) | \([2]\) | \(4423680\) | \(2.2141\) | \(\Gamma_0(N)\)-optimal |
| 366912.dn1 | 366912dn2 | \([0, 0, 0, -5119716, -4457474336]\) | \(42246001231552/14414517\) | \(5063791448795369472\) | \([2]\) | \(8847360\) | \(2.5606\) |
Rank
sage: E.rank()
The elliptic curves in class 366912dn have rank \(1\).
Complex multiplication
The elliptic curves in class 366912dn do not have complex multiplication.Modular form 366912.2.a.dn
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.
