Properties

Label 176400.tn
Number of curves $2$
Conductor $176400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("tn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 176400.tn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.tn1 176400gy2 \([0, 0, 0, -61831875, 198003181250]\) \(-7620530425/526848\) \(-1807428372664320000000000\) \([]\) \(29859840\) \(3.4054\)  
176400.tn2 176400gy1 \([0, 0, 0, 4318125, 280831250]\) \(2595575/1512\) \(-5187134998080000000000\) \([]\) \(9953280\) \(2.8561\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 176400.tn have rank \(0\).

Complex multiplication

The elliptic curves in class 176400.tn do not have complex multiplication.

Modular form 176400.2.a.tn

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.