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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 15246n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15246.o2 | 15246n1 | \([1, -1, 0, -15912, 765760]\) | \(459206250875/7375872\) | \(7156801225728\) | \([2]\) | \(30720\) | \(1.2664\) | \(\Gamma_0(N)\)-optimal |
15246.o1 | 15246n2 | \([1, -1, 0, -31752, -998816]\) | \(3648707754875/1660262688\) | \(1610951225903712\) | \([2]\) | \(61440\) | \(1.6130\) |
Rank
sage: E.rank()
The elliptic curves in class 15246n have rank \(1\).
Complex multiplication
The elliptic curves in class 15246n do not have complex multiplication.Modular form 15246.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.