Properties

Label 56784.c
Number of curves $2$
Conductor $56784$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 56784.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56784.c1 56784ci1 \([0, -1, 0, -31857232, 69219276736]\) \(-82318551880501/54432\) \(-2364309954032173056\) \([]\) \(3744000\) \(2.8425\) \(\Gamma_0(N)\)-optimal
56784.c2 56784ci2 \([0, -1, 0, 65689568, 357910138624]\) \(721710134999099/1691848015872\) \(-73487160211562160325656576\) \([]\) \(18720000\) \(3.6473\)  

Rank

sage: E.rank()
 

The elliptic curves in class 56784.c have rank \(0\).

Complex multiplication

The elliptic curves in class 56784.c do not have complex multiplication.

Modular form 56784.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} + q^{7} + q^{9} - 5 q^{11} + 3 q^{15} - 3 q^{17} + q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.