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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 46200.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46200.z1 | 46200v2 | \([0, -1, 0, -868, 10132]\) | \(2262732176/1617\) | \(51744000\) | \([2]\) | \(23552\) | \(0.41557\) | |
46200.z2 | 46200v1 | \([0, -1, 0, -43, 232]\) | \(-4499456/7623\) | \(-15246000\) | \([2]\) | \(11776\) | \(0.068997\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46200.z have rank \(1\).
Complex multiplication
The elliptic curves in class 46200.z do not have complex multiplication.Modular form 46200.2.a.z
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.