Properties

Label 4025.f
Number of curves $4$
Conductor $4025$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 4025.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4025.f1 4025c4 \([1, -1, 0, -1052192, 415686091]\) \(8244966675515989329/3081640625\) \(48150634765625\) \([2]\) \(34560\) \(1.9766\)  
4025.f2 4025c3 \([1, -1, 0, -137942, -10015159]\) \(18577831198352049/7958740140575\) \(124355314696484375\) \([2]\) \(34560\) \(1.9766\)  
4025.f3 4025c2 \([1, -1, 0, -66067, 6444216]\) \(2041085246738049/38897700625\) \(607776572265625\) \([2, 2]\) \(17280\) \(1.6301\)  
4025.f4 4025c1 \([1, -1, 0, 58, 294591]\) \(1367631/2399636575\) \(-37494321484375\) \([2]\) \(8640\) \(1.2835\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4025.f have rank \(0\).

Complex multiplication

The elliptic curves in class 4025.f do not have complex multiplication.

Modular form 4025.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{7} - 3 q^{8} - 3 q^{9} - 4 q^{11} + 2 q^{13} + q^{14} - q^{16} - 6 q^{17} - 3 q^{18} + 4 q^{19} + O(q^{20})\)  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.