# Properties

 Label 32340.q Number of curves $4$ Conductor $32340$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 32340.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.q1 32340p4 $$[0, -1, 0, -76260, 4428600]$$ $$1628514404944/664335375$$ $$20008548488544000$$ $$$$ $$248832$$ $$1.8256$$
32340.q2 32340p2 $$[0, -1, 0, -35100, -2519208]$$ $$158792223184/16335$$ $$491979882240$$ $$$$ $$82944$$ $$1.2763$$
32340.q3 32340p1 $$[0, -1, 0, -2025, -45198]$$ $$-488095744/200475$$ $$-377370932400$$ $$$$ $$41472$$ $$0.92968$$ $$\Gamma_0(N)$$-optimal
32340.q4 32340p3 $$[0, -1, 0, 15615, 496350]$$ $$223673040896/187171875$$ $$-352329342750000$$ $$$$ $$124416$$ $$1.4790$$

## Rank

sage: E.rank()

The elliptic curves in class 32340.q have rank $$0$$.

## Complex multiplication

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

## Modular form 32340.2.a.q

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} - q^{11} + 4q^{13} - q^{15} + 6q^{17} - 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 