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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 33488n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33488.e2 | 33488n1 | \([0, 1, 0, 272, 1812]\) | \(541343375/625807\) | \(-2563305472\) | \([2]\) | \(15360\) | \(0.49173\) | \(\Gamma_0(N)\)-optimal |
33488.e1 | 33488n2 | \([0, 1, 0, -1568, 15796]\) | \(104154702625/32188247\) | \(131843059712\) | \([2]\) | \(30720\) | \(0.83830\) |
Rank
sage: E.rank()
The elliptic curves in class 33488n have rank \(1\).
Complex multiplication
The elliptic curves in class 33488n do not have complex multiplication.Modular form 33488.2.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.