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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 122100x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 122100.ba2 | 122100x1 | \([0, 1, 0, -245333, 46491588]\) | \(6532108386304000/31987847133\) | \(7996961783250000\) | \([2]\) | \(829440\) | \(1.8995\) | \(\Gamma_0(N)\)-optimal |
| 122100.ba1 | 122100x2 | \([0, 1, 0, -3920708, 2986791588]\) | \(1666315860501346000/40252707\) | \(161010828000000\) | \([2]\) | \(1658880\) | \(2.2461\) |
Rank
sage: E.rank()
The elliptic curves in class 122100x have rank \(1\).
Complex multiplication
The elliptic curves in class 122100x do not have complex multiplication.Modular form 122100.2.a.x
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.
