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Properties

Label 148225ch
Number of curves $2$
Conductor $148225$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ch1")
 
E.isogeny_class()
 

Elliptic curves in class 148225ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
148225.cj2 148225ch1 \([1, 0, 1, -47556, 4342083]\) \(-9317\) \(-1276587078045125\) \([]\) \(483840\) \(1.6369\) \(\Gamma_0(N)\)-optimal
148225.cj1 148225ch2 \([1, 0, 1, -1233724231, -16679304303917]\) \(-162677523113838677\) \(-1276587078045125\) \([]\) \(17902080\) \(3.4424\)  

Rank

sage: E.rank()
 

The elliptic curves in class 148225ch have rank \(1\).

Complex multiplication

The elliptic curves in class 148225ch do not have complex multiplication.

Modular form 148225.2.a.ch

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

\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.