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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 248430v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
248430.v1 | 248430v1 | \([1, 1, 0, -1138634123, -14788983971523]\) | \(98610250747761380828647/47309184000\) | \(78324871524052608000\) | \([2]\) | \(72253440\) | \(3.5896\) | \(\Gamma_0(N)\)-optimal |
248430.v2 | 248430v2 | \([1, 1, 0, -1138444843, -14794146356387]\) | \(-98561081716303113792487/68303188804500000\) | \(-113082451132439125291500000\) | \([2]\) | \(144506880\) | \(3.9361\) |
Rank
sage: E.rank()
The elliptic curves in class 248430v have rank \(0\).
Complex multiplication
The elliptic curves in class 248430v do not have complex multiplication.Modular form 248430.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.