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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 248430.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 248430.k1 | 248430k1 | \([1, 1, 0, -896127313, 10324926739093]\) | \(307903452713493241418533/1106380800000\) | \(285971614642022400000\) | \([2]\) | \(61931520\) | \(3.5665\) | \(\Gamma_0(N)\)-optimal |
| 248430.k2 | 248430k2 | \([1, 1, 0, -895719633, 10334790882837]\) | \(-307483415359033331264293/583686101250000000\) | \(-150868179218736866250000000\) | \([2]\) | \(123863040\) | \(3.9131\) |
Rank
sage: E.rank()
The elliptic curves in class 248430.k have rank \(1\).
Complex multiplication
The elliptic curves in class 248430.k do not have complex multiplication.Modular form 248430.2.a.k
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 LMFDB 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 LMFDB labels.
