Show commands:
SageMath
E = EllipticCurve("nw1")
E.isogeny_class()
Elliptic curves in class 327600nw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
327600.nw1 | 327600nw1 | \([0, 0, 0, -107175, 12491750]\) | \(46689225424/3901625\) | \(11377138500000000\) | \([2]\) | \(2654208\) | \(1.8228\) | \(\Gamma_0(N)\)-optimal |
327600.nw2 | 327600nw2 | \([0, 0, 0, 113325, 57253250]\) | \(13799183324/129390625\) | \(-1509212250000000000\) | \([2]\) | \(5308416\) | \(2.1694\) |
Rank
sage: E.rank()
The elliptic curves in class 327600nw have rank \(0\).
Complex multiplication
The elliptic curves in class 327600nw do not have complex multiplication.Modular form 327600.2.a.nw
sage: E.q_eigenform(10)
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.