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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 100016.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100016.g1 | 100016m1 | \([0, 0, 0, -5171, -142350]\) | \(3733252610697/23278724\) | \(95349653504\) | \([2]\) | \(80640\) | \(0.94455\) | \(\Gamma_0(N)\)-optimal |
| 100016.g2 | 100016m2 | \([0, 0, 0, -2131, -308334]\) | \(-261284780457/9875692358\) | \(-40450835898368\) | \([2]\) | \(161280\) | \(1.2911\) |
Rank
sage: E.rank()
The elliptic curves in class 100016.g have rank \(1\).
Complex multiplication
The elliptic curves in class 100016.g do not have complex multiplication.Modular form 100016.2.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.
