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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 101430g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101430.j2 | 101430g1 | \([1, -1, 0, -121359240, 511872654656]\) | \(62228632040416581492843/382900201062400000\) | \(1216291295379338035200000\) | \([2]\) | \(20275200\) | \(3.4599\) | \(\Gamma_0(N)\)-optimal |
101430.j1 | 101430g2 | \([1, -1, 0, -195117960, -183657323200]\) | \(258620799050621485981803/145075171220000000000\) | \(460834618109268060000000000\) | \([2]\) | \(40550400\) | \(3.8064\) |
Rank
sage: E.rank()
The elliptic curves in class 101430g have rank \(1\).
Complex multiplication
The elliptic curves in class 101430g do not have complex multiplication.Modular form 101430.2.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 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.