Properties

Label 148800ei
Number of curves $2$
Conductor $148800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ei1")
 
E.isogeny_class()
 

Elliptic curves in class 148800ei

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
148800.bc2 148800ei1 \([0, -1, 0, 747967, 93875937]\) \(11298232190519/7472736000\) \(-30608326656000000000\) \([2]\) \(4423680\) \(2.4278\) \(\Gamma_0(N)\)-optimal
148800.bc1 148800ei2 \([0, -1, 0, -3220033, 780339937]\) \(901456690969801/457629750000\) \(1874451456000000000000\) \([2]\) \(8847360\) \(2.7743\)  

Rank

sage: E.rank()
 

The elliptic curves in class 148800ei have rank \(1\).

Complex multiplication

The elliptic curves in class 148800ei do not have complex multiplication.

Modular form 148800.2.a.ei

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