Properties

 Label 462e Number of curves $2$ Conductor $462$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

Elliptic curves in class 462e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462.e2 462e1 $$[1, 1, 1, -405, 4731]$$ $$-7347774183121/6119866368$$ $$-6119866368$$ $$$$ $$672$$ $$0.57576$$ $$\Gamma_0(N)$$-optimal
462.e1 462e2 $$[1, 1, 1, -7445, 244091]$$ $$45637459887836881/13417633152$$ $$13417633152$$ $$$$ $$1344$$ $$0.92233$$

Rank

sage: E.rank()

The elliptic curves in class 462e have rank $$1$$.

Complex multiplication

The elliptic curves in class 462e do not have complex multiplication.

Modular form462.2.a.e

sage: E.q_eigenform(10)

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