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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 13860s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13860.o2 | 13860s1 | \([0, 0, 0, -192, -3211]\) | \(-67108864/343035\) | \(-4001160240\) | \([2]\) | \(7680\) | \(0.52680\) | \(\Gamma_0(N)\)-optimal |
13860.o1 | 13860s2 | \([0, 0, 0, -4647, -121714]\) | \(59466754384/121275\) | \(22632825600\) | \([2]\) | \(15360\) | \(0.87338\) |
Rank
sage: E.rank()
The elliptic curves in class 13860s have rank \(0\).
Complex multiplication
The elliptic curves in class 13860s do not have complex multiplication.Modular form 13860.2.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.