Properties

Label 3025g
Number of curves $3$
Conductor $3025$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3025g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3025.a3 3025g1 \([0, 1, 1, -1008, -29606]\) \(-4096/11\) \(-304487046875\) \([]\) \(3360\) \(0.89094\) \(\Gamma_0(N)\)-optimal
3025.a2 3025g2 \([0, 1, 1, -31258, 3842394]\) \(-122023936/161051\) \(-4457994853296875\) \([]\) \(16800\) \(1.6957\)  
3025.a1 3025g3 \([0, 1, 1, -23656508, 44278891894]\) \(-52893159101157376/11\) \(-304487046875\) \([]\) \(84000\) \(2.5004\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3025g have rank \(0\).

Complex multiplication

The elliptic curves in class 3025g do not have complex multiplication.

Modular form 3025.2.a.g

sage: E.q_eigenform(10)
 
\(q - 2q^{2} + q^{3} + 2q^{4} - 2q^{6} - 2q^{7} - 2q^{9} + 2q^{12} + 4q^{13} + 4q^{14} - 4q^{16} - 2q^{17} + 4q^{18} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.