Properties

Label 3025.f
Number of curves $4$
Conductor $3025$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3025.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3025.f1 3025b3 \([1, -1, 0, -179042, -29107259]\) \(22930509321/6875\) \(190304404296875\) \([2]\) \(11520\) \(1.7180\)  
3025.f2 3025b4 \([1, -1, 0, -88292, 9884991]\) \(2749884201/73205\) \(2026361296953125\) \([2]\) \(11520\) \(1.7180\)  
3025.f3 3025b2 \([1, -1, 0, -12667, -324384]\) \(8120601/3025\) \(83733937890625\) \([2, 2]\) \(5760\) \(1.3714\)  
3025.f4 3025b1 \([1, -1, 0, 2458, -37009]\) \(59319/55\) \(-1522435234375\) \([2]\) \(2880\) \(1.0249\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3025.2.a.f

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.