Properties

Label 1350.q
Number of curves $2$
Conductor $1350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 1350.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1350.q1 1350t2 \([1, -1, 1, -1805, 30197]\) \(-6847995/64\) \(-6075000000\) \([3]\) \(1080\) \(0.69899\)  
1350.q2 1350t1 \([1, -1, 1, 70, 197]\) \(3645/4\) \(-42187500\) \([]\) \(360\) \(0.14969\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1350.q have rank \(0\).

Complex multiplication

The elliptic curves in class 1350.q do not have complex multiplication.

Modular form 1350.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} + 2 q^{13} - q^{14} + q^{16} + 6 q^{17} - q^{19} + O(q^{20})\) 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.