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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 76230x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76230.a1 | 76230x1 | \([1, -1, 0, -1260, 50166]\) | \(-2509090441/10718750\) | \(-945490218750\) | \([]\) | \(155520\) | \(0.98297\) | \(\Gamma_0(N)\)-optimal |
76230.a2 | 76230x2 | \([1, -1, 0, 11115, -1204659]\) | \(1721540467559/8070721400\) | \(-711910263972600\) | \([]\) | \(466560\) | \(1.5323\) |
Rank
sage: E.rank()
The elliptic curves in class 76230x have rank \(1\).
Complex multiplication
The elliptic curves in class 76230x do not have complex multiplication.Modular form 76230.2.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.