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Properties

Label 4025b
Number of curves $2$
Conductor $4025$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 4025b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4025.g1 4025b1 \([1, -1, 0, -4067, -98784]\) \(476196576129/197225\) \(3081640625\) \([2]\) \(3456\) \(0.78270\) \(\Gamma_0(N)\)-optimal
4025.g2 4025b2 \([1, -1, 0, -3442, -130659]\) \(-288673724529/311181605\) \(-4862212578125\) \([2]\) \(6912\) \(1.1293\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4025.2.a.b

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