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SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 224400.eq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
224400.eq1 | 224400bg2 | \([0, 1, 0, -3714008, -1896204012]\) | \(88526309511756241/26991954000000\) | \(1727485056000000000000\) | \([2]\) | \(12386304\) | \(2.7800\) | |
224400.eq2 | 224400bg1 | \([0, 1, 0, 637992, -198924012]\) | \(448733772344879/527357952000\) | \(-33750908928000000000\) | \([2]\) | \(6193152\) | \(2.4334\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 224400.eq have rank \(0\).
Complex multiplication
The elliptic curves in class 224400.eq do not have complex multiplication.Modular form 224400.2.a.eq
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.