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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 112710ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
112710.y1 | 112710ba1 | \([1, 0, 1, -129381694, -566452339024]\) | \(9923129938500427467001/59574528000000\) | \(1437984280242432000000\) | \([2]\) | \(15482880\) | \(3.2480\) | \(\Gamma_0(N)\)-optimal |
112710.y2 | 112710ba2 | \([1, 0, 1, -126977214, -588517771088]\) | \(-9380102000370554601721/770302406250000000\) | \(-18593227481725406250000000\) | \([2]\) | \(30965760\) | \(3.5946\) |
Rank
sage: E.rank()
The elliptic curves in class 112710ba have rank \(1\).
Complex multiplication
The elliptic curves in class 112710ba do not have complex multiplication.Modular form 112710.2.a.ba
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.