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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 17424.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17424.n1 | 17424bx2 | \([0, 0, 0, -1407351, -642598814]\) | \(932410994128/29403\) | \(9721096369281792\) | \([2]\) | \(230400\) | \(2.1636\) | |
17424.n2 | 17424bx1 | \([0, 0, 0, -84216, -10934165]\) | \(-3196715008/649539\) | \(-13421741009860656\) | \([2]\) | \(115200\) | \(1.8170\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17424.n have rank \(0\).
Complex multiplication
The elliptic curves in class 17424.n do not have complex multiplication.Modular form 17424.2.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.