↑

Properties

Label 435600.ip
Number of curves $2$
Conductor $435600$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("ip1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 435600.ip have rank \(1\).

Complex multiplication

The elliptic curves in class 435600.ip do not have complex multiplication.

Modular form 435600.2.a.ip

Copy content sage:E.q_eigenform(10)
 
\(q - q^{7} + 4 q^{13} + 3 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 435600.ip

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435600.ip1 435600ip1 \([0, 0, 0, -149964375, -706862488750]\) \(-2888047810000/35937\) \(-4641148440195300000000\) \([]\) \(49766400\) \(3.3046\) \(\Gamma_0(N)\)-optimal*
435600.ip2 435600ip2 \([0, 0, 0, -68289375, -1470344053750]\) \(-272709010000/7073843073\) \(-913564174651202873700000000\) \([]\) \(149299200\) \(3.8539\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 435600.ip1.