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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 126852.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126852.n1 | 126852l2 | \([0, 1, 0, -14200055372, 651298404349428]\) | \(1393746203803968446127568/335238123\) | \(76166417452551875328\) | \([2]\) | \(70041600\) | \(4.1017\) | |
| 126852.n2 | 126852l1 | \([0, 1, 0, -887500157, 10176395239200]\) | \(-5444260314792559771648/84436212706659\) | \(-1198999193389741371388464\) | \([2]\) | \(35020800\) | \(3.7552\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 126852.n have rank \(1\).
Complex multiplication
The elliptic curves in class 126852.n do not have complex multiplication.Modular form 126852.2.a.n
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.
