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Properties

Label 462400.p
Number of curves $2$
Conductor $462400$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("p1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 462400.p have rank \(1\).

Complex multiplication

The elliptic curves in class 462400.p do not have complex multiplication.

Modular form 462400.2.a.p

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

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 462400.p

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462400.p1 462400p2 \([0, 0, 0, -58312888300, -5420199028082000]\) \(-45145776875761017/2441406250\) \(-1185878764970000000000000000000\) \([]\) \(2541846528\) \(4.8374\)  
462400.p2 462400p1 \([0, 0, 0, -64360300, 292490542000]\) \(-60698457/40960\) \(-19895744189714923520000000\) \([]\) \(195526656\) \(3.5550\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 462400.p1.