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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 121242.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121242.t1 | 121242x2 | \([1, 1, 1, -922809, -336911409]\) | \(49057238215631017/773195636664\) | \(1369763235284112504\) | \([2]\) | \(2741760\) | \(2.2807\) | |
| 121242.t2 | 121242x1 | \([1, 1, 1, -114529, 6769247]\) | \(93780867197737/42939243072\) | \(76069488395875392\) | \([2]\) | \(1370880\) | \(1.9341\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 121242.t have rank \(1\).
Complex multiplication
The elliptic curves in class 121242.t do not have complex multiplication.Modular form 121242.2.a.t
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.
