Properties

Label 4160i
Number of curves $2$
Conductor $4160$
CM no
Rank $1$
Graph

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

Elliptic curves in class 4160i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4160.c1 4160i1 \([0, 1, 0, -53825, -4823777]\) \(65787589563409/10400000\) \(2726297600000\) \([2]\) \(15360\) \(1.3967\) \(\Gamma_0(N)\)-optimal
4160.c2 4160i2 \([0, 1, 0, -48705, -5773025]\) \(-48743122863889/26406250000\) \(-6922240000000000\) \([2]\) \(30720\) \(1.7432\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4160i have rank \(1\).

Complex multiplication

The elliptic curves in class 4160i do not have complex multiplication.

Modular form 4160.2.a.i

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{5} - 4 q^{7} + q^{9} + 2 q^{11} + q^{13} - 2 q^{15} + 2 q^{17} - 6 q^{19} + O(q^{20})\) 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.