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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 3024n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3024.ba2 | 3024n1 | \([0, 0, 0, -216, -1188]\) | \(221184/7\) | \(35271936\) | \([]\) | \(864\) | \(0.22289\) | \(\Gamma_0(N)\)-optimal |
3024.ba1 | 3024n2 | \([0, 0, 0, -2376, 44172]\) | \(32710656/343\) | \(15554923776\) | \([]\) | \(2592\) | \(0.77219\) |
Rank
sage: E.rank()
The elliptic curves in class 3024n have rank \(0\).
Complex multiplication
The elliptic curves in class 3024n do not have complex multiplication.Modular form 3024.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.