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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 12696.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12696.n1 | 12696l1 | \([0, -1, 0, -105447, -13075920]\) | \(4499456/27\) | \(778097949752016\) | \([2]\) | \(52992\) | \(1.6967\) | \(\Gamma_0(N)\)-optimal |
| 12696.n2 | 12696l2 | \([0, -1, 0, -44612, -28114332]\) | \(-21296/729\) | \(-336138314292870912\) | \([2]\) | \(105984\) | \(2.0433\) |
Rank
sage: E.rank()
The elliptic curves in class 12696.n have rank \(1\).
Complex multiplication
The elliptic curves in class 12696.n do not have complex multiplication.Modular form 12696.2.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.
