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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 178608s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
178608.j2 | 178608s1 | \([0, -1, 0, -298920, -485353872]\) | \(-13997521/474336\) | \(-100097918127715516416\) | \([]\) | \(5356800\) | \(2.5180\) | \(\Gamma_0(N)\)-optimal |
178608.j1 | 178608s2 | \([0, -1, 0, -30662280, 82145851248]\) | \(-15107691357361/5067577806\) | \(-1069398039218647170932736\) | \([]\) | \(26784000\) | \(3.3227\) |
Rank
sage: E.rank()
The elliptic curves in class 178608s have rank \(0\).
Complex multiplication
The elliptic curves in class 178608s do not have complex multiplication.Modular form 178608.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.