Show commands:
SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 36400bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36400.o2 | 36400bz1 | \([0, 1, 0, -2933, -62237]\) | \(-43614208/91\) | \(-5824000000\) | \([]\) | \(31104\) | \(0.75936\) | \(\Gamma_0(N)\)-optimal |
36400.o3 | 36400bz2 | \([0, 1, 0, 5067, -302237]\) | \(224755712/753571\) | \(-48228544000000\) | \([]\) | \(93312\) | \(1.3087\) | |
36400.o1 | 36400bz3 | \([0, 1, 0, -46933, 9629763]\) | \(-178643795968/524596891\) | \(-33574201024000000\) | \([]\) | \(279936\) | \(1.8580\) |
Rank
sage: E.rank()
The elliptic curves in class 36400bz have rank \(1\).
Complex multiplication
The elliptic curves in class 36400bz do not have complex multiplication.Modular form 36400.2.a.bz
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.