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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 12696.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12696.s1 | 12696p2 | \([0, 1, 0, -63069672, -192808566720]\) | \(15043017316604/243\) | \(448184419057161216\) | \([2]\) | \(1059840\) | \(2.9324\) | |
12696.s2 | 12696p1 | \([0, 1, 0, -3938052, -3019719168]\) | \(-14647977776/59049\) | \(-27227203457722543872\) | \([2]\) | \(529920\) | \(2.5858\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12696.s have rank \(0\).
Complex multiplication
The elliptic curves in class 12696.s do not have complex multiplication.Modular form 12696.2.a.s
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.