Properties

Label 96600.c
Number of curves $2$
Conductor $96600$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 96600.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96600.c1 96600t2 \([0, -1, 0, -73288, 7660972]\) \(170054560416634/1633023\) \(418053888000\) \([2]\) \(251904\) \(1.3916\)  
96600.c2 96600t1 \([0, -1, 0, -4688, 114972]\) \(89036727188/8117781\) \(1039075968000\) \([2]\) \(125952\) \(1.0450\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 96600.c have rank \(0\).

Complex multiplication

The elliptic curves in class 96600.c do not have complex multiplication.

Modular form 96600.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - 4 q^{11} + 2 q^{17} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.