# Properties

 Label 3450.c Number of curves $2$ Conductor $3450$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 3450.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.c1 3450a2 $$[1, 1, 0, -19650, -742500]$$ $$53706380371489/16171875000$$ $$252685546875000$$ $$$$ $$11520$$ $$1.4688$$
3450.c2 3450a1 $$[1, 1, 0, 3350, -75500]$$ $$265971760991/317400000$$ $$-4959375000000$$ $$$$ $$5760$$ $$1.1222$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3450.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3450.c do not have complex multiplication.

## Modular form3450.2.a.c

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 