Properties

Label 6400i
Number of curves $2$
Conductor $6400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 6400i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6400.s2 6400i1 \([0, 1, 0, 67, -37]\) \(1600\) \(-20480000\) \([]\) \(1152\) \(0.091987\) \(\Gamma_0(N)\)-optimal
6400.s1 6400i2 \([0, 1, 0, -6333, 191963]\) \(-2194880\) \(-12800000000\) \([]\) \(5760\) \(0.89671\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6400i have rank \(0\).

Complex multiplication

The elliptic curves in class 6400i do not have complex multiplication.

Modular form 6400.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{7} - 2 q^{9} + 5 q^{11} + 6 q^{13} - 3 q^{17} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.