# Properties

 Label 463680gp Number of curves $2$ Conductor $463680$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("gp1")

sage: E.isogeny_class()

## Elliptic curves in class 463680gp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.gp1 463680gp1 $$[0, 0, 0, -348, -688]$$ $$10536048/5635$$ $$2492743680$$ $$$$ $$245760$$ $$0.49432$$ $$\Gamma_0(N)$$-optimal
463680.gp2 463680gp2 $$[0, 0, 0, 1332, -5392]$$ $$147704148/92575$$ $$-163808870400$$ $$$$ $$491520$$ $$0.84089$$

## Rank

sage: E.rank()

The elliptic curves in class 463680gp have rank $$1$$.

## Complex multiplication

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

## Modular form 463680.2.a.gp

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} + 4q^{11} - 4q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$ ## 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. 