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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 3570b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3570.a2 | 3570b1 | \([1, 1, 0, 470267, 1634976973]\) | \(11501534367688741509671/1161179873437500000000\) | \(-1161179873437500000000\) | \([2]\) | \(215040\) | \(2.7214\) | \(\Gamma_0(N)\)-optimal |
3570.a1 | 3570b2 | \([1, 1, 0, -18279733, 29073726973]\) | \(675512349748162449958490329/25568496800736303750000\) | \(25568496800736303750000\) | \([2]\) | \(430080\) | \(3.0680\) |
Rank
sage: E.rank()
The elliptic curves in class 3570b have rank \(0\).
Complex multiplication
The elliptic curves in class 3570b do not have complex multiplication.Modular form 3570.2.a.b
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.