Properties

 Label 10626.s Number of curves $2$ Conductor $10626$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

Elliptic curves in class 10626.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10626.s1 10626q2 $$[1, 0, 0, -62068, 5946650]$$ $$26444015547214434625/46191222$$ $$46191222$$ $$$$ $$21504$$ $$1.1586$$
10626.s2 10626q1 $$[1, 0, 0, -3878, 92736]$$ $$-6449916994998625/8532911772$$ $$-8532911772$$ $$$$ $$10752$$ $$0.81201$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 10626.s have rank $$0$$.

Complex multiplication

The elliptic curves in class 10626.s do not have complex multiplication.

Modular form 10626.2.a.s

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} + q^{9} - q^{11} + q^{12} + 6 q^{13} + q^{14} + q^{16} + 4 q^{17} + q^{18} - 2 q^{19} + O(q^{20})$$ 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 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. 