Properties

 Label 101430dr Number of curves $4$ Conductor $101430$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dr1")

sage: E.isogeny_class()

Elliptic curves in class 101430dr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.dn3 101430dr1 $$[1, -1, 1, -56061473, 173052650481]$$ $$-227196402372228188089/19338934824115200$$ $$-1658625424136177961139200$$ $$[2]$$ $$17694720$$ $$3.3922$$ $$\Gamma_0(N)$$-optimal
101430.dn2 101430dr2 $$[1, -1, 1, -914564993, 10645765390257]$$ $$986396822567235411402169/6336721794060000$$ $$543476048132687041260000$$ $$[2]$$ $$35389440$$ $$3.7387$$
101430.dn4 101430dr3 $$[1, -1, 1, 332364712, 6314936667]$$ $$47342661265381757089751/27397579603968000000$$ $$-2349784127421051568128000000$$ $$[2]$$ $$53084160$$ $$3.9415$$
101430.dn1 101430dr4 $$[1, -1, 1, -1329464408, 51516688731]$$ $$3029968325354577848895529/1753440696000000000000$$ $$150385806899460216000000000000$$ $$[2]$$ $$106168320$$ $$4.2880$$

Rank

sage: E.rank()

The elliptic curves in class 101430dr have rank $$0$$.

Complex multiplication

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

Modular form 101430.2.a.dr

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 4q^{13} + q^{16} - 2q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.