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Properties

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

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Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 148225.cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
148225.cm1 148225co2 \([1, 1, 0, -7636675, 7495068750]\) \(15124197817/1294139\) \(4214492664781224546875\) \([2]\) \(8847360\) \(2.8906\)  
148225.cm2 148225co1 \([1, 1, 0, 515700, 541092875]\) \(4657463/41503\) \(-135158656888027609375\) \([2]\) \(4423680\) \(2.5440\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 148225.2.a.cm

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