# Properties

 Label 30960w Number of curves $2$ Conductor $30960$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

## Elliptic curves in class 30960w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.c2 30960w1 $$[0, 0, 0, -1250043, 537879658]$$ $$1953326569433829507/262451171875$$ $$29025000000000000$$ $$[2]$$ $$573440$$ $$2.1778$$ $$\Gamma_0(N)$$-optimal
30960.c1 30960w2 $$[0, 0, 0, -20000043, 34426629658]$$ $$8000051600110940079507/144453125$$ $$15975360000000$$ $$[2]$$ $$1146880$$ $$2.5244$$

## Rank

sage: E.rank()

The elliptic curves in class 30960w have rank $$1$$.

## Complex multiplication

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

## Modular form 30960.2.a.w

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{7} + 4q^{11} + 2q^{13} - 6q^{17} + 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.