Properties

 Label 462d Number of curves $2$ Conductor $462$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

Elliptic curves in class 462d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462.d2 462d1 $$[1, 0, 1, -1676, 5058506]$$ $$-520203426765625/11054534935707648$$ $$-11054534935707648$$ $$$$ $$4160$$ $$1.7574$$ $$\Gamma_0(N)$$-optimal
462.d1 462d2 $$[1, 0, 1, -452236, 115355594]$$ $$10228636028672744397625/167006381634183168$$ $$167006381634183168$$ $$$$ $$8320$$ $$2.1039$$

Rank

sage: E.rank()

The elliptic curves in class 462d have rank $$0$$.

Complex multiplication

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

Modular form462.2.a.d

sage: E.q_eigenform(10)

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