Properties

Label 3025.e
Number of curves $2$
Conductor $3025$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 3025.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3025.e1 3025c2 \([1, 0, 1, -7626, 1001273]\) \(-121\) \(-405272259390625\) \([]\) \(9240\) \(1.4857\)  
3025.e2 3025c1 \([1, 0, 1, -751, -7977]\) \(-24729001\) \(-1890625\) \([]\) \(840\) \(0.28676\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3025.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - 2 q^{7} - 3 q^{8} + q^{9} + 2 q^{12} + q^{13} - 2 q^{14} - q^{16} - 5 q^{17} + q^{18} - 6 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.