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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 114800.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 114800.g1 | 114800by2 | \([0, 0, 0, -3844525075, 91751286039250]\) | \(98191033604529537629349729/10906239337336\) | \(697999317589504000000\) | \([]\) | \(82978560\) | \(3.8686\) | |
| 114800.g2 | 114800by1 | \([0, 0, 0, -7741075, -7631000750]\) | \(801581275315909089/70810888830976\) | \(4531896885182464000000\) | \([]\) | \(11854080\) | \(2.8957\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 114800.g have rank \(1\).
Complex multiplication
The elliptic curves in class 114800.g do not have complex multiplication.Modular form 114800.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
