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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 15138v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15138.s2 | 15138v1 | \([1, -1, 1, 37687, -4686775]\) | \(13651919/29696\) | \(-12876963665163264\) | \([]\) | \(100800\) | \(1.7754\) | \(\Gamma_0(N)\)-optimal |
15138.s1 | 15138v2 | \([1, -1, 1, -3444053, 2477642465]\) | \(-10418796526321/82044596\) | \(-35576686476798197364\) | \([]\) | \(504000\) | \(2.5801\) |
Rank
sage: E.rank()
The elliptic curves in class 15138v have rank \(1\).
Complex multiplication
The elliptic curves in class 15138v do not have complex multiplication.Modular form 15138.2.a.v
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.