Properties

Label 101430.dz
Number of curves $2$
Conductor $101430$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 101430.dz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.dz1 101430cz1 \([1, -1, 1, -241403483, 603658895627]\) \(489781415227546051766883/233890092903563264000\) \(742957259580305490051072000\) \([2]\) \(49545216\) \(3.8499\) \(\Gamma_0(N)\)-optimal
101430.dz2 101430cz2 \([1, -1, 1, 866482597, 4590719320331]\) \(22649115256119592694355357/15973509811739648000000\) \(-50740221307716661883904000000\) \([2]\) \(99090432\) \(4.1965\)  

Rank

sage: E.rank()
 

The elliptic curves in class 101430.dz have rank \(0\).

Complex multiplication

The elliptic curves in class 101430.dz do not have complex multiplication.

Modular form 101430.2.a.dz

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 2q^{11} + 6q^{13} + q^{16} + 6q^{17} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.