Show commands:
SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 44100dj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44100.s2 | 44100dj1 | \([0, 0, 0, 18375, -2786875]\) | \(1280/7\) | \(-3752267793750000\) | \([]\) | \(207360\) | \(1.6705\) | \(\Gamma_0(N)\)-optimal |
44100.s1 | 44100dj2 | \([0, 0, 0, -1084125, -434966875]\) | \(-262885120/343\) | \(-183861121893750000\) | \([]\) | \(622080\) | \(2.2198\) |
Rank
sage: E.rank()
The elliptic curves in class 44100dj have rank \(1\).
Complex multiplication
The elliptic curves in class 44100dj do not have complex multiplication.Modular form 44100.2.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 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.