Properties

Label 1840.c
Number of curves $2$
Conductor $1840$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1840.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1840.c1 1840f1 \([0, -1, 0, -46, -529]\) \(-687518464/7604375\) \(-121670000\) \([]\) \(576\) \(0.23342\) \(\Gamma_0(N)\)-optimal
1840.c2 1840f2 \([0, -1, 0, 414, 13915]\) \(489277573376/5615234375\) \(-89843750000\) \([]\) \(1728\) \(0.78273\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1840.c have rank \(0\).

Complex multiplication

The elliptic curves in class 1840.c do not have complex multiplication.

Modular form 1840.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + 4q^{7} - 2q^{9} + 6q^{11} - q^{13} + q^{15} - 2q^{19} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.