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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 2358x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2358.y2 | 2358x1 | \([1, -1, 1, -356, -2491]\) | \(6826561273/7074\) | \(5156946\) | \([]\) | \(1216\) | \(0.20573\) | \(\Gamma_0(N)\)-optimal |
2358.y1 | 2358x2 | \([1, -1, 1, -1301, 15653]\) | \(333822098953/53954184\) | \(39332600136\) | \([3]\) | \(3648\) | \(0.75504\) |
Rank
sage: E.rank()
The elliptic curves in class 2358x have rank \(0\).
Complex multiplication
The elliptic curves in class 2358x do not have complex multiplication.Modular form 2358.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.