Properties

 Label 369600.vd Number of curves $2$ Conductor $369600$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("vd1")

sage: E.isogeny_class()

Elliptic curves in class 369600.vd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.vd1 369600vd2 $$[0, 1, 0, -1793, 22143]$$ $$77860436/17787$$ $$145711104000$$ $$$$ $$294912$$ $$0.85456$$
369600.vd2 369600vd1 $$[0, 1, 0, -593, -5457]$$ $$11279504/693$$ $$1419264000$$ $$$$ $$147456$$ $$0.50799$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 369600.vd have rank $$0$$.

Complex multiplication

The elliptic curves in class 369600.vd do not have complex multiplication.

Modular form 369600.2.a.vd

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} + q^{11} - 4 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})$$ 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 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. 