Properties

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

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 96600.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96600.t1 96600k1 \([0, -1, 0, -57384908, 167336029812]\) \(5224645130090610708304/67370009765625\) \(269480039062500000000\) \([2]\) \(10321920\) \(3.0654\) \(\Gamma_0(N)\)-optimal
96600.t2 96600k2 \([0, -1, 0, -55822408, 176876654812]\) \(-1202345928696155427076/148724718496003125\) \(-2379595495936050000000000\) \([2]\) \(20643840\) \(3.4120\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 96600.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} + 6 q^{11} + 4 q^{13} - 2 q^{17} - 8 q^{19} + O(q^{20})\) 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.