Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 96600d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96600.g2 96600d1 \([0, -1, 0, -4923408, 4206454812]\) \(824899990643380516/312440625\) \(4999050000000000\) \([2]\) \(1658880\) \(2.3627\) \(\Gamma_0(N)\)-optimal
96600.g1 96600d2 \([0, -1, 0, -4946408, 4165192812]\) \(418257395996078018/8023271484375\) \(256744687500000000000\) \([2]\) \(3317760\) \(2.7093\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 96600.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - 2 q^{11} + 2 q^{13} - 4 q^{17} - 2 q^{19} + O(q^{20})\) 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 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.