Properties

Label 101430l
Number of curves $2$
Conductor $101430$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 101430l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.cf1 101430l1 \([1, -1, 0, -62484, 5913088]\) \(8493409990827/185150000\) \(588133233450000\) \([2]\) \(491520\) \(1.6223\) \(\Gamma_0(N)\)-optimal
101430.cf2 101430l2 \([1, -1, 0, 5136, 17990020]\) \(4716275733/44023437500\) \(-139841461757812500\) \([2]\) \(983040\) \(1.9689\)  

Rank

sage: E.rank()
 

The elliptic curves in class 101430l have rank \(1\).

Complex multiplication

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

Modular form 101430.2.a.l

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 Cremona 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 Cremona labels.