Properties

Label 1425.g
Number of curves $2$
Conductor $1425$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1425.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1425.g1 1425c2 \([1, 1, 0, -1900, -2375]\) \(48587168449/28048275\) \(438254296875\) \([2]\) \(1920\) \(0.92336\)  
1425.g2 1425c1 \([1, 1, 0, 475, 0]\) \(756058031/438615\) \(-6853359375\) \([2]\) \(960\) \(0.57679\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1425.g have rank \(0\).

Complex multiplication

The elliptic curves in class 1425.g do not have complex multiplication.

Modular form 1425.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{6} + 2 q^{7} - 3 q^{8} + q^{9} - 6 q^{11} + q^{12} + 2 q^{14} - q^{16} + 6 q^{17} + q^{18} + q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.