# Properties

 Label 460.c Number of curves $2$ Conductor $460$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("c1")

E.isogeny_class()

## Elliptic curves in class 460.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
460.c1 460c1 $$[0, 1, 0, -46, 529]$$ $$-687518464/7604375$$ $$-121670000$$ $$$$ $$144$$ $$0.23342$$ $$\Gamma_0(N)$$-optimal
460.c2 460c2 $$[0, 1, 0, 414, -13915]$$ $$489277573376/5615234375$$ $$-89843750000$$ $$[]$$ $$432$$ $$0.78273$$

## Rank

sage: E.rank()

The elliptic curves in class 460.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 460.c do not have complex multiplication.

## Modular form460.2.a.c

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - 4 q^{7} - 2 q^{9} - 6 q^{11} - q^{13} - q^{15} + 2 q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 