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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 102850m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102850.ba2 | 102850m1 | \([1, -1, 0, 1617808, 156201216]\) | \(16917195186711/10172800000\) | \(-281589620950000000000\) | \([2]\) | \(3456000\) | \(2.6132\) | \(\Gamma_0(N)\)-optimal |
102850.ba1 | 102850m2 | \([1, -1, 0, -6610192, 1266981216]\) | \(1153957554747369/642812500000\) | \(17793461801757812500000\) | \([2]\) | \(6912000\) | \(2.9598\) |
Rank
sage: E.rank()
The elliptic curves in class 102850m have rank \(1\).
Complex multiplication
The elliptic curves in class 102850m do not have complex multiplication.Modular form 102850.2.a.m
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.