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Properties

Label 381150.cu
Number of curves $2$
Conductor $381150$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("cu1")
 
E.isogeny_class()
 

Elliptic curves in class 381150.cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381150.cu1 381150cu2 \([1, -1, 0, -381717, -95947659]\) \(-7620530425/526848\) \(-425254572832320000\) \([]\) \(5598720\) \(2.1336\)  
381150.cu2 381150cu1 \([1, -1, 0, 26658, -142884]\) \(2595575/1512\) \(-1220437230705000\) \([]\) \(1866240\) \(1.5843\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 381150.cu have rank \(0\).

Complex multiplication

The elliptic curves in class 381150.cu do not have complex multiplication.

Modular form 381150.2.a.cu

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} + q^{13} + q^{14} + q^{16} + 3 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.