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SageMath
E = EllipticCurve("oc1")
E.isogeny_class()
Elliptic curves in class 176400.oc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.oc1 | 176400kl2 | \([0, 0, 0, -35166075, 80266030250]\) | \(68971442301/400\) | \(27892413158400000000\) | \([2]\) | \(8257536\) | \(2.9214\) | |
176400.oc2 | 176400kl1 | \([0, 0, 0, -2238075, 1205902250]\) | \(17779581/1280\) | \(89255722106880000000\) | \([2]\) | \(4128768\) | \(2.5749\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.oc have rank \(1\).
Complex multiplication
The elliptic curves in class 176400.oc do not have complex multiplication.Modular form 176400.2.a.oc
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.