Properties

 Label 348726c Number of curves $2$ Conductor $348726$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

Elliptic curves in class 348726c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
348726.c1 348726c1 [1, 1, 0, -560612209656, -161523012846271680] [2] 7280824320 $$\Gamma_0(N)$$-optimal
348726.c2 348726c2 [1, 1, 0, -488690381816, -204488005201738944] [2] 14561648640

Rank

sage: E.rank()

The elliptic curves in class 348726c have rank $$0$$.

Complex multiplication

The elliptic curves in class 348726c do not have complex multiplication.

Modular form 348726.2.a.c

sage: E.q_eigenform(10)

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

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.