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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 48139.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48139.g1 | 48139h3 | \([0, 1, 1, -62069, 14648769]\) | \(-178643795968/524596891\) | \(-77659167125821099\) | \([]\) | \(449064\) | \(1.9279\) | |
48139.g2 | 48139h1 | \([0, 1, 1, -3879, -94461]\) | \(-43614208/91\) | \(-13471265899\) | \([]\) | \(49896\) | \(0.82924\) | \(\Gamma_0(N)\)-optimal |
48139.g3 | 48139h2 | \([0, 1, 1, 6701, -460000]\) | \(224755712/753571\) | \(-111555552909619\) | \([]\) | \(149688\) | \(1.3785\) |
Rank
sage: E.rank()
The elliptic curves in class 48139.g have rank \(1\).
Complex multiplication
The elliptic curves in class 48139.g do not have complex multiplication.Modular form 48139.2.a.g
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 LMFDB numbering.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.