Properties

Label 148120.i
Number of curves $2$
Conductor $148120$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 148120.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
148120.i1 148120e2 \([0, 1, 0, -15497760, -22899437600]\) \(1357792998752738/38897700625\) \(11792907657375192320000\) \([2]\) \(12976128\) \(3.0134\)  
148120.i2 148120e1 \([0, 1, 0, -2272760, 810342400]\) \(8564808605476/3081640625\) \(467142051328400000000\) \([2]\) \(6488064\) \(2.6668\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 148120.i have rank \(1\).

Complex multiplication

The elliptic curves in class 148120.i do not have complex multiplication.

Modular form 148120.2.a.i

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{5} + q^{7} + q^{9} + 6 q^{11} + 4 q^{13} - 2 q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.