Properties

Label 344760cn
Number of curves $2$
Conductor $344760$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 344760cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
344760.cn1 344760cn1 \([0, 1, 0, -47491760, 125767815408]\) \(2396726313900986596/4154072495625\) \(20532136456740055680000\) \([2]\) \(30965760\) \(3.1752\) \(\Gamma_0(N)\)-optimal
344760.cn2 344760cn2 \([0, 1, 0, -32640040, 205872052400]\) \(-389032340685029858/1627263833203125\) \(-16085999033301693600000000\) \([2]\) \(61931520\) \(3.5218\)  

Rank

sage: E.rank()
 

The elliptic curves in class 344760cn have rank \(1\).

Complex multiplication

The elliptic curves in class 344760cn do not have complex multiplication.

Modular form 344760.2.a.cn

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} - 2 q^{11} + q^{15} - q^{17} + 8 q^{19} + O(q^{20})\) 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 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.