Properties

 Label 4620h Number of curves $2$ Conductor $4620$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

Elliptic curves in class 4620h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4620.h2 4620h1 $$[0, 1, 0, -82321, -12507496]$$ $$-3856034557002072064/1973796785296875$$ $$-31580748564750000$$ $$$$ $$40320$$ $$1.8706$$ $$\Gamma_0(N)$$-optimal
4620.h1 4620h2 $$[0, 1, 0, -1449196, -671887996]$$ $$1314817350433665559504/190690249278375$$ $$48816703815264000$$ $$$$ $$80640$$ $$2.2172$$

Rank

sage: E.rank()

The elliptic curves in class 4620h have rank $$1$$.

Complex multiplication

The elliptic curves in class 4620h do not have complex multiplication.

Modular form4620.2.a.h

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - q^{7} + q^{9} - q^{11} - q^{15} - 2 q^{17} - 6 q^{19} + O(q^{20})$$ 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. 