# Properties

 Label 463680ip Number of curves $2$ Conductor $463680$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ip1")

sage: E.isogeny_class()

## Elliptic curves in class 463680ip

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.ip1 463680ip1 $$[0, 0, 0, -2837722572, -24326957092464]$$ $$489781415227546051766883/233890092903563264000$$ $$1206821505891260360376188928000$$ $$$$ $$594542592$$ $$4.4660$$ $$\Gamma_0(N)$$-optimal
463680.ip2 463680ip2 $$[0, 0, 0, 10185591348, -185029441539696]$$ $$22649115256119592694355357/15973509811739648000000$$ $$-82419802079093454689796096000000$$ $$$$ $$1189085184$$ $$4.8126$$

## Rank

sage: E.rank()

The elliptic curves in class 463680ip have rank $$0$$.

## Complex multiplication

The elliptic curves in class 463680ip do not have complex multiplication.

## Modular form 463680.2.a.ip

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} - 2q^{11} + 6q^{13} + 6q^{17} + O(q^{20})$$ ## 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. 