Show commands:
SageMath
E = EllipticCurve("kd1")
E.isogeny_class()
Elliptic curves in class 346560kd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
346560.kd1 | 346560kd1 | \([0, 1, 0, -832225, -336756577]\) | \(-14317849/2700\) | \(-12020775704513740800\) | \([]\) | \(9455616\) | \(2.3852\) | \(\Gamma_0(N)\)-optimal |
346560.kd2 | 346560kd2 | \([0, 1, 0, 5752415, 1650487775]\) | \(4728305591/3000000\) | \(-13356417449459712000000\) | \([]\) | \(28366848\) | \(2.9345\) |
Rank
sage: E.rank()
The elliptic curves in class 346560kd have rank \(0\).
Complex multiplication
The elliptic curves in class 346560kd do not have complex multiplication.Modular form 346560.2.a.kd
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.