# Properties

 Label 3450.i Number of curves $2$ Conductor $3450$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 3450.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.i1 3450l2 $$[1, 0, 1, -66701, -4248952]$$ $$84013940106985/28705554432$$ $$11213107200000000$$ $$[]$$ $$25920$$ $$1.7817$$
3450.i2 3450l1 $$[1, 0, 1, -27326, 1736048]$$ $$5776556465785/1073088$$ $$419175000000$$ $$[3]$$ $$8640$$ $$1.2324$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3450.2.a.i

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} - 3q^{11} + q^{12} - q^{13} + q^{14} + q^{16} + 6q^{17} - q^{18} - q^{19} + O(q^{20})$$

## 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.