Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 103600e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
103600.bd1 | 103600e1 | \([0, 0, 0, -422050, 105534375]\) | \(33256413948450816/2481997\) | \(620499250000\) | \([2]\) | \(391680\) | \(1.7125\) | \(\Gamma_0(N)\)-optimal |
103600.bd2 | 103600e2 | \([0, 0, 0, -421175, 105993750]\) | \(-2065624967846736/17960084863\) | \(-71840339452000000\) | \([2]\) | \(783360\) | \(2.0590\) |
Rank
sage: E.rank()
The elliptic curves in class 103600e have rank \(0\).
Complex multiplication
The elliptic curves in class 103600e do not have complex multiplication.Modular form 103600.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.