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Properties

Label 25350dm
Number of curves $2$
Conductor $25350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dm1")
 
E.isogeny_class()
 

Elliptic curves in class 25350dm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25350.dm2 25350dm1 \([1, 0, 0, -37594138, -88723846108]\) \(623295446073461/5458752\) \(51461627504625000000\) \([2]\) \(2580480\) \(2.9491\) \(\Gamma_0(N)\)-optimal
25350.dm1 25350dm2 \([1, 0, 0, -38439138, -84526731108]\) \(666276475992821/58199166792\) \(548664574343997515625000\) \([2]\) \(5160960\) \(3.2957\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25350dm have rank \(0\).

Complex multiplication

The elliptic curves in class 25350dm do not have complex multiplication.

Modular form 25350.2.a.dm

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + 4 q^{7} + q^{8} + q^{9} - 2 q^{11} + q^{12} + 4 q^{14} + q^{16} - 4 q^{17} + q^{18} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.