# Properties

 Label 30960v Number of curves $2$ Conductor $30960$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 30960v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.y2 30960v1 $$[0, 0, 0, -123, -22]$$ $$1860867/1075$$ $$118886400$$ $$$$ $$8192$$ $$0.23898$$ $$\Gamma_0(N)$$-optimal
30960.y1 30960v2 $$[0, 0, 0, -1323, 18458]$$ $$2315685267/9245$$ $$1022423040$$ $$$$ $$16384$$ $$0.58555$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 30960.2.a.v

sage: E.q_eigenform(10)

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