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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 179776.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179776.g1 | 179776d1 | \([0, 1, 0, -194757, 32974747]\) | \(35995648/53\) | \(1202904207193088\) | \([2]\) | \(943488\) | \(1.7950\) | \(\Gamma_0(N)\)-optimal |
179776.g2 | 179776d2 | \([0, 1, 0, -138577, 52446735]\) | \(-810448/2809\) | \(-1020062767699738624\) | \([2]\) | \(1886976\) | \(2.1416\) |
Rank
sage: E.rank()
The elliptic curves in class 179776.g have rank \(0\).
Complex multiplication
The elliptic curves in class 179776.g do not have complex multiplication.Modular form 179776.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.