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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 227154.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227154.s1 | 227154b1 | \([1, 0, 0, -20525, -1127919]\) | \(39616946929/226368\) | \(5463973219392\) | \([2]\) | \(1474560\) | \(1.2856\) | \(\Gamma_0(N)\)-optimal |
227154.s2 | 227154b2 | \([1, 0, 0, -8965, -2387959]\) | \(-3301293169/100082952\) | \(-2415759159623688\) | \([2]\) | \(2949120\) | \(1.6321\) |
Rank
sage: E.rank()
The elliptic curves in class 227154.s have rank \(0\).
Complex multiplication
The elliptic curves in class 227154.s do not have complex multiplication.Modular form 227154.2.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.