# Properties

 Label 1960b Number of curves $4$ Conductor $1960$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 1960b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1960.g3 1960b1 $$[0, 0, 0, -98, -343]$$ $$55296/5$$ $$9411920$$ $$$$ $$288$$ $$0.077594$$ $$\Gamma_0(N)$$-optimal
1960.g2 1960b2 $$[0, 0, 0, -343, 2058]$$ $$148176/25$$ $$752953600$$ $$[2, 2]$$ $$576$$ $$0.42417$$
1960.g1 1960b3 $$[0, 0, 0, -5243, 146118]$$ $$132304644/5$$ $$602362880$$ $$$$ $$1152$$ $$0.77074$$
1960.g4 1960b4 $$[0, 0, 0, 637, 11662]$$ $$237276/625$$ $$-75295360000$$ $$$$ $$1152$$ $$0.77074$$

## Rank

sage: E.rank()

The elliptic curves in class 1960b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1960b do not have complex multiplication.

## Modular form1960.2.a.b

sage: E.q_eigenform(10)

$$q - q^{5} - 3 q^{9} + 4 q^{11} + 2 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})$$ ## 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. 