Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 344760.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
344760.f1 344760f2 \([0, -1, 0, -5199886696, -144243368318804]\) \(715954183155446306906/453598627601025\) \(9851261669352919258434201600\) \([2]\) \(360222720\) \(4.3127\)  
344760.f2 344760f1 \([0, -1, 0, -5199095776, -144289465350980]\) \(1431255071664791409172/575042085\) \(6244386232147059409920\) \([2]\) \(180111360\) \(3.9661\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 344760.2.a.f

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