# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("bi1")

sage: E.isogeny_class()

## Elliptic curves in class 30960bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.d2 30960bi1 $$[0, 0, 0, 357, -6838]$$ $$1685159/7740$$ $$-23111516160$$ $$$$ $$21504$$ $$0.67103$$ $$\Gamma_0(N)$$-optimal
30960.d1 30960bi2 $$[0, 0, 0, -3963, -85462]$$ $$2305199161/277350$$ $$828162662400$$ $$$$ $$43008$$ $$1.0176$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 30960.2.a.bi

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{7} + 4q^{11} + 4q^{13} + O(q^{20})$$ ## 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. 