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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 67600z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67600.s2 | 67600z1 | \([0, 1, 0, -14083, 249588]\) | \(2048\) | \(150837781250000\) | \([2]\) | \(172800\) | \(1.4140\) | \(\Gamma_0(N)\)-optimal |
67600.s1 | 67600z2 | \([0, 1, 0, -119708, -15805412]\) | \(78608\) | \(2413404500000000\) | \([2]\) | \(345600\) | \(1.7605\) |
Rank
sage: E.rank()
The elliptic curves in class 67600z have rank \(0\).
Complex multiplication
The elliptic curves in class 67600z do not have complex multiplication.Modular form 67600.2.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 Cremona 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 Cremona labels.