Show commands:
SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 15680.dj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15680.dj1 | 15680bj2 | \([0, -1, 0, -31425, -2133823]\) | \(-5452947409/250\) | \(-157351936000\) | \([]\) | \(34560\) | \(1.2241\) | |
| 15680.dj2 | 15680bj1 | \([0, -1, 0, -65, -7615]\) | \(-49/40\) | \(-25176309760\) | \([]\) | \(11520\) | \(0.67480\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15680.dj have rank \(0\).
Complex multiplication
The elliptic curves in class 15680.dj do not have complex multiplication.Modular form 15680.2.a.dj
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.
