Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2116.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2116.d1 | 2116c2 | \([0, 1, 0, -9698, 446045]\) | \(-42592000/12167\) | \(-28818442583408\) | \([]\) | \(3168\) | \(1.2978\) | |
| 2116.d2 | 2116c1 | \([0, 1, 0, 882, -4663]\) | \(32000/23\) | \(-54477207152\) | \([]\) | \(1056\) | \(0.74848\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2116.d have rank \(1\).
Complex multiplication
The elliptic curves in class 2116.d do not have complex multiplication.Modular form 2116.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
