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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 215600.ch
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215600.ch1 | 215600bx1 | \([0, -1, 0, -1735008, 888608512]\) | \(-76711450249/851840\) | \(-6413959946240000000\) | \([]\) | \(3773952\) | \(2.4236\) | \(\Gamma_0(N)\)-optimal |
215600.ch2 | 215600bx2 | \([0, -1, 0, 5810992, 4601240512]\) | \(2882081488391/2883584000\) | \(-21712049537024000000000\) | \([]\) | \(11321856\) | \(2.9729\) |
Rank
sage: E.rank()
The elliptic curves in class 215600.ch have rank \(1\).
Complex multiplication
The elliptic curves in class 215600.ch do not have complex multiplication.Modular form 215600.2.a.ch
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.