Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 344760.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
344760.f1 | 344760f2 | \([0, -1, 0, -5199886696, -144243368318804]\) | \(715954183155446306906/453598627601025\) | \(9851261669352919258434201600\) | \([2]\) | \(360222720\) | \(4.3127\) | |
344760.f2 | 344760f1 | \([0, -1, 0, -5199095776, -144289465350980]\) | \(1431255071664791409172/575042085\) | \(6244386232147059409920\) | \([2]\) | \(180111360\) | \(3.9661\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 344760.f have rank \(1\).
Complex multiplication
The elliptic curves in class 344760.f do not have complex multiplication.Modular form 344760.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.