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SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 244800.eq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
244800.eq1 | 244800eq2 | \([0, 0, 0, -20100, -1096000]\) | \(19248832/17\) | \(793152000000\) | \([2]\) | \(393216\) | \(1.2086\) | |
244800.eq2 | 244800eq1 | \([0, 0, 0, -975, -25000]\) | \(-140608/289\) | \(-210681000000\) | \([2]\) | \(196608\) | \(0.86201\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 244800.eq have rank \(0\).
Complex multiplication
The elliptic curves in class 244800.eq do not have complex multiplication.Modular form 244800.2.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.