# Properties

 Label 30960s Number of curves $4$ Conductor $30960$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 30960s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.z4 30960s1 $$[0, 0, 0, -327723, -72179878]$$ $$35198225176082067/18035507200$$ $$1994582812262400$$ $$[2]$$ $$221184$$ $$1.8873$$ $$\Gamma_0(N)$$-optimal
30960.z2 30960s2 $$[0, 0, 0, -5242923, -4620705958]$$ $$144118734029937784467/37867520$$ $$4187844771840$$ $$[2]$$ $$442368$$ $$2.2339$$
30960.z3 30960s3 $$[0, 0, 0, -1003563, 300642138]$$ $$1386456968640843/318028000000$$ $$25639916027904000000$$ $$[2]$$ $$663552$$ $$2.4366$$
30960.z1 30960s4 $$[0, 0, 0, -5323563, -4471229862]$$ $$206956783279200843/12642726098000$$ $$1019276401815281664000$$ $$[2]$$ $$1327104$$ $$2.7832$$

## Rank

sage: E.rank()

The elliptic curves in class 30960s have rank $$0$$.

## Complex multiplication

The elliptic curves in class 30960s do not have complex multiplication.

## Modular form 30960.2.a.s

sage: E.q_eigenform(10)

$$q - q^{5} + 4q^{7} + 2q^{13} + 6q^{17} - 2q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.