# Properties

 Label 32340t Number of curves $2$ Conductor $32340$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 32340t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.t2 32340t1 $$[0, -1, 0, 12675, -1379223]$$ $$7476617216/31444875$$ $$-947061273312000$$ $$[]$$ $$124416$$ $$1.5563$$ $$\Gamma_0(N)$$-optimal
32340.t1 32340t2 $$[0, -1, 0, -116685, 42189225]$$ $$-5833703071744/22107421875$$ $$-665834515500000000$$ $$[]$$ $$373248$$ $$2.1056$$

## Rank

sage: E.rank()

The elliptic curves in class 32340t have rank $$1$$.

## Complex multiplication

The elliptic curves in class 32340t do not have complex multiplication.

## Modular form 32340.2.a.t

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} + q^{11} - 2 q^{13} - q^{15} + 3 q^{17} + 7 q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 