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Properties

Label 201243d
Number of curves $2$
Conductor $201243$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 201243d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
201243.b2 201243d1 \([0, -1, 1, -3194, -74446]\) \(-28672/3\) \(-377161782123\) \([]\) \(309960\) \(0.96037\) \(\Gamma_0(N)\)-optimal
201243.b1 201243d2 \([0, -1, 1, -1248984, 538106834]\) \(-1713910976512/1594323\) \(-200439234653229243\) \([]\) \(4029480\) \(2.2428\)  

Rank

sage: E.rank()
 

The elliptic curves in class 201243d have rank \(0\).

Complex multiplication

The elliptic curves in class 201243d do not have complex multiplication.

Modular form 201243.2.a.d

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + q^{9} + 4 q^{10} - 2 q^{11} - 2 q^{12} + q^{13} + 2 q^{15} - 4 q^{16} - 2 q^{18} + q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.