Show commands:
SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 44100.dj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44100.dj1 | 44100m2 | \([0, 0, 0, -959175, -354233250]\) | \(10536048/245\) | \(2269371561660000000\) | \([2]\) | \(663552\) | \(2.3081\) | |
44100.dj2 | 44100m1 | \([0, 0, 0, -132300, 10418625]\) | \(442368/175\) | \(101311230431250000\) | \([2]\) | \(331776\) | \(1.9615\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44100.dj have rank \(1\).
Complex multiplication
The elliptic curves in class 44100.dj 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 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.