Properties

Label 101430.db
Number of curves $2$
Conductor $101430$
CM no
Rank $0$
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Show commands for: SageMath
sage: E = EllipticCurve("db1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 101430.db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.db1 101430da1 \([1, -1, 1, -562358, -159091019]\) \(8493409990827/185150000\) \(428749127185050000\) \([2]\) \(1474560\) \(2.1716\) \(\Gamma_0(N)\)-optimal
101430.db2 101430da2 \([1, -1, 1, 46222, -485776763]\) \(4716275733/44023437500\) \(-101944425621445312500\) \([2]\) \(2949120\) \(2.5182\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 101430.2.a.db

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} - 2q^{11} - 2q^{13} + q^{16} + 2q^{17} + 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.