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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 13680s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13680.b2 | 13680s1 | \([0, 0, 0, 42, 43]\) | \(702464/475\) | \(-5540400\) | \([2]\) | \(3072\) | \(-0.017351\) | \(\Gamma_0(N)\)-optimal |
13680.b1 | 13680s2 | \([0, 0, 0, -183, 358]\) | \(3631696/1805\) | \(336856320\) | \([2]\) | \(6144\) | \(0.32922\) |
Rank
sage: E.rank()
The elliptic curves in class 13680s have rank \(1\).
Complex multiplication
The elliptic curves in class 13680s do not have complex multiplication.Modular form 13680.2.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 Cremona 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 Cremona labels.