Properties

Label 62400cr
Number of curves $4$
Conductor $62400$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cr1")
 
E.isogeny_class()
 

Elliptic curves in class 62400cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.fy4 62400cr1 \([0, 1, 0, -2308, -6862]\) \(1360251712/771147\) \(771147000000\) \([2]\) \(98304\) \(0.97086\) \(\Gamma_0(N)\)-optimal
62400.fy2 62400cr2 \([0, 1, 0, -23433, 1366263]\) \(22235451328/123201\) \(7884864000000\) \([2, 2]\) \(196608\) \(1.3174\)  
62400.fy3 62400cr3 \([0, 1, 0, -10433, 2887263]\) \(-245314376/6908733\) \(-3537271296000000\) \([2]\) \(393216\) \(1.6640\)  
62400.fy1 62400cr4 \([0, 1, 0, -374433, 88063263]\) \(11339065490696/351\) \(179712000000\) \([2]\) \(393216\) \(1.6640\)  

Rank

sage: E.rank()
 

The elliptic curves in class 62400cr have rank \(1\).

Complex multiplication

The elliptic curves in class 62400cr do not have complex multiplication.

Modular form 62400.2.a.cr

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} + 4 q^{11} + q^{13} + 6 q^{17} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.