Show commands:
SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 380880.dj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 380880.dj1 | 380880dj2 | \([0, 0, 0, -4077003, -2895672998]\) | \(33909572018/3234375\) | \(714849912248544000000\) | \([2]\) | \(22708224\) | \(2.7394\) | |
| 380880.dj2 | 380880dj1 | \([0, 0, 0, 303117, -215915582]\) | \(27871484/198375\) | \(-21922063975622016000\) | \([2]\) | \(11354112\) | \(2.3928\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 380880.dj have rank \(1\).
Complex multiplication
The elliptic curves in class 380880.dj do not have complex multiplication.Modular form 380880.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
