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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 52020.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
52020.s1 | 52020w1 | \([0, 0, 0, -72828, -7561107]\) | \(151732224/85\) | \(23930951409360\) | \([2]\) | \(221184\) | \(1.5144\) | \(\Gamma_0(N)\)-optimal |
52020.s2 | 52020w2 | \([0, 0, 0, -59823, -10346778]\) | \(-5256144/7225\) | \(-32546093916729600\) | \([2]\) | \(442368\) | \(1.8609\) |
Rank
sage: E.rank()
The elliptic curves in class 52020.s have rank \(1\).
Complex multiplication
The elliptic curves in class 52020.s do not have complex multiplication.Modular form 52020.2.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.