Properties

 Label 100010f Number of curves 2 Conductor 100010 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100010.j1")

sage: E.isogeny_class()

Elliptic curves in class 100010f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100010.j2 100010f1 [1, 1, 1, -120, 245] [2] 45056 $$\Gamma_0(N)$$-optimal
100010.j1 100010f2 [1, 1, 1, -850, -9683] [2] 90112

Rank

sage: E.rank()

The elliptic curves in class 100010f have rank $$1$$.

Modular form 100010.2.a.j

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} + q^{5} + 2q^{6} - 4q^{7} + q^{8} + q^{9} + q^{10} + 4q^{11} + 2q^{12} - 2q^{13} - 4q^{14} + 2q^{15} + q^{16} - 2q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.