Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 22800.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22800.f1 | 22800bt2 | \([0, -1, 0, -86908, -8871188]\) | \(18148802937424/1947796875\) | \(7791187500000000\) | \([2]\) | \(110592\) | \(1.7835\) | |
22800.f2 | 22800bt1 | \([0, -1, 0, -84533, -9431688]\) | \(267219216891904/3655125\) | \(913781250000\) | \([2]\) | \(55296\) | \(1.4369\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22800.f have rank \(0\).
Complex multiplication
The elliptic curves in class 22800.f do not have complex multiplication.Modular form 22800.2.a.f
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.