Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 201898.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
201898.c1 | 201898i2 | \([1, 1, 0, -1583927, 771817753]\) | \(-10418796526321/82044596\) | \(-3460684841640254036\) | \([]\) | \(4176000\) | \(2.3859\) | |
201898.c2 | 201898i1 | \([1, 1, 0, 17333, -1451587]\) | \(13651919/29696\) | \(-1252593127003136\) | \([]\) | \(835200\) | \(1.5812\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 201898.c have rank \(0\).
Complex multiplication
The elliptic curves in class 201898.c do not have complex multiplication.Modular form 201898.2.a.c
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.