Properties

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

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 381150.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381150.t1 381150t1 \([1, -1, 0, -3812067, -8293001909]\) \(-2509090441/10718750\) \(-26171774959671386718750\) \([]\) \(41057280\) \(2.9866\) \(\Gamma_0(N)\)-optimal
381150.t2 381150t2 \([1, -1, 0, 33622308, 199954426216]\) \(1721540467559/8070721400\) \(-19706132174274425446875000\) \([]\) \(123171840\) \(3.5359\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 381150.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} - 5 q^{13} + q^{14} + q^{16} + 5 q^{19} + O(q^{20})\) 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.