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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 277200z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.z1 | 277200z1 | \([0, 0, 0, -93075, -10104750]\) | \(51603494067/4336640\) | \(7493713920000000\) | \([2]\) | \(1474560\) | \(1.7878\) | \(\Gamma_0(N)\)-optimal |
277200.z2 | 277200z2 | \([0, 0, 0, 98925, -46392750]\) | \(61958108493/573927200\) | \(-991746201600000000\) | \([2]\) | \(2949120\) | \(2.1344\) |
Rank
sage: E.rank()
The elliptic curves in class 277200z have rank \(0\).
Complex multiplication
The elliptic curves in class 277200z do not have complex multiplication.Modular form 277200.2.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.