Properties

Label 381150.oh
Number of curves $2$
Conductor $381150$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("oh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 381150.oh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381150.oh1 381150oh2 \([1, -1, 1, -9542930, -12003000303]\) \(-7620530425/526848\) \(-6644602700505000000000\) \([]\) \(27993600\) \(2.9383\)  
381150.oh2 381150oh1 \([1, -1, 1, 666445, -17194053]\) \(2595575/1512\) \(-19069331729765625000\) \([]\) \(9331200\) \(2.3890\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 381150.oh have rank \(1\).

Complex multiplication

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

Modular form 381150.2.a.oh

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