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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 49005.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49005.g1 | 49005b2 | \([0, 0, 1, -13068, 548039]\) | \(2359296/125\) | \(13076113186125\) | \([]\) | \(97200\) | \(1.2736\) | |
49005.g2 | 49005b1 | \([0, 0, 1, -2178, -38932]\) | \(884736/5\) | \(6457339845\) | \([]\) | \(32400\) | \(0.72431\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 49005.g have rank \(0\).
Complex multiplication
The elliptic curves in class 49005.g do not have complex multiplication.Modular form 49005.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.