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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 145728.dv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145728.dv1 | 145728fj2 | \([0, 0, 0, -713100, 229975792]\) | \(209849322390625/1882056627\) | \(359666622420221952\) | \([2]\) | \(1310720\) | \(2.1915\) | |
145728.dv2 | 145728fj1 | \([0, 0, 0, -13260, 8546416]\) | \(-1349232625/164333367\) | \(-31404595489800192\) | \([2]\) | \(655360\) | \(1.8449\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 145728.dv have rank \(1\).
Complex multiplication
The elliptic curves in class 145728.dv do not have complex multiplication.Modular form 145728.2.a.dv
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.