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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 143325.dn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
143325.dn1 | 143325dt2 | \([0, 0, 1, -463050, 121840031]\) | \(-303464448/1625\) | \(-58796696232421875\) | \([]\) | \(1306368\) | \(2.0623\) | |
143325.dn2 | 143325dt1 | \([0, 0, 1, 14700, 889656]\) | \(7077888/10985\) | \(-545220393046875\) | \([]\) | \(435456\) | \(1.5130\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 143325.dn have rank \(1\).
Complex multiplication
The elliptic curves in class 143325.dn do not have complex multiplication.Modular form 143325.2.a.dn
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.