Properties

Label 12696.c
Number of curves $2$
Conductor $12696$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 12696.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12696.c1 12696n1 \([0, -1, 0, -199, 1144]\) \(4499456/27\) \(5256144\) \([2]\) \(2304\) \(0.12899\) \(\Gamma_0(N)\)-optimal
12696.c2 12696n2 \([0, -1, 0, -84, 2340]\) \(-21296/729\) \(-2270654208\) \([2]\) \(4608\) \(0.47557\)  

Rank

sage: E.rank()
 

The elliptic curves in class 12696.c have rank \(1\).

Complex multiplication

The elliptic curves in class 12696.c do not have complex multiplication.

Modular form 12696.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{5} - 2q^{7} + q^{9} + 2q^{13} + 2q^{15} + 6q^{17} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.