# Properties

 Label 30960e Number of curves $4$ Conductor $30960$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 30960e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.m4 30960e1 $$[0, 0, 0, -8103, 358022]$$ $$-315278049616/114259815$$ $$-21323623714560$$ $$$$ $$67584$$ $$1.2681$$ $$\Gamma_0(N)$$-optimal
30960.m3 30960e2 $$[0, 0, 0, -139323, 20014778]$$ $$400649568576484/33698025$$ $$25155440870400$$ $$[2, 2]$$ $$135168$$ $$1.6147$$
30960.m2 30960e3 $$[0, 0, 0, -149043, 17061842]$$ $$245245463376482/57692266875$$ $$86134092906240000$$ $$$$ $$270336$$ $$1.9613$$
30960.m1 30960e4 $$[0, 0, 0, -2229123, 1281000098]$$ $$820480625548035842/5805$$ $$8666818560$$ $$$$ $$270336$$ $$1.9613$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 30960.2.a.e

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 