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Properties

Label 54390.l
Number of curves $2$
Conductor $54390$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 54390.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54390.l1 54390m2 \([1, 1, 0, -167752, 26392024]\) \(-4437543642183289/3191139000\) \(-375434312211000\) \([]\) \(456192\) \(1.7318\)  
54390.l2 54390m1 \([1, 1, 0, 2033, 155611]\) \(7892485271/92517390\) \(-10884578416110\) \([]\) \(152064\) \(1.1825\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54390.l have rank \(2\).

Complex multiplication

The elliptic curves in class 54390.l do not have complex multiplication.

Modular form 54390.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} - q^{12} + q^{13} - q^{15} + q^{16} - 6 q^{17} - q^{18} - 8 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.