Show commands:
SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 104400et
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
104400.bp2 | 104400et1 | \([0, 0, 0, 17925, 1534250]\) | \(13651919/29696\) | \(-1385496576000000\) | \([]\) | \(403200\) | \(1.5896\) | \(\Gamma_0(N)\)-optimal |
104400.bp1 | 104400et2 | \([0, 0, 0, -1638075, -812425750]\) | \(-10418796526321/82044596\) | \(-3827872670976000000\) | \([]\) | \(2016000\) | \(2.3943\) |
Rank
sage: E.rank()
The elliptic curves in class 104400et have rank \(0\).
Complex multiplication
The elliptic curves in class 104400et do not have complex multiplication.Modular form 104400.2.a.et
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.