# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 30960.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.t1 30960t2 $$[0, 0, 0, -1421523, 597112722]$$ $$3940344055317123/369800000000$$ $$29813855846400000000$$ $$$$ $$663552$$ $$2.4751$$
30960.t2 30960t1 $$[0, 0, 0, -315603, -57813102]$$ $$43121696645763/7045120000$$ $$567988621148160000$$ $$$$ $$331776$$ $$2.1285$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 30960.2.a.t

sage: E.q_eigenform(10)

$$q - q^{5} + 2q^{7} - 2q^{11} + 2q^{13} + 8q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 