Properties

Label 49725h
Number of curves $4$
Conductor $49725$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 49725h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
49725.u4 49725h1 \([1, -1, 0, 51061833, -221933622384]\) \(1292603583867446566871/2615843353271484375\) \(-29796090695858001708984375\) \([2]\) \(11501568\) \(3.5725\) \(\Gamma_0(N)\)-optimal
49725.u3 49725h2 \([1, -1, 0, -388391292, -2377451200509]\) \(568832774079017834683129/114800389711906640625\) \(1307648189062186578369140625\) \([2, 2]\) \(23003136\) \(3.9190\)  
49725.u2 49725h3 \([1, -1, 0, -1933156917, 30595571065116]\) \(70141892778055497175333129/5090453819946781723125\) \(57983450542831310564970703125\) \([2]\) \(46006272\) \(4.2656\)  
49725.u1 49725h4 \([1, -1, 0, -5874875667, -173308871903634]\) \(1968666709544018637994033129/113621848881699526875\) \(1294223872418108673310546875\) \([2]\) \(46006272\) \(4.2656\)  

Rank

sage: E.rank()
 

The elliptic curves in class 49725h have rank \(1\).

Complex multiplication

The elliptic curves in class 49725h do not have complex multiplication.

Modular form 49725.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 4 q^{7} - 3 q^{8} + 4 q^{11} - q^{13} - 4 q^{14} - q^{16} + q^{17} + O(q^{20})\) 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.