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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 28611d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28611.u1 | 28611d1 | \([1, -1, 0, -19128, -670909]\) | \(1187648379/384659\) | \(250687795157217\) | \([2]\) | \(82944\) | \(1.4663\) | \(\Gamma_0(N)\)-optimal |
28611.u2 | 28611d2 | \([1, -1, 0, 54567, -4635700]\) | \(27570978261/30116537\) | \(-19627379726720931\) | \([2]\) | \(165888\) | \(1.8129\) |
Rank
sage: E.rank()
The elliptic curves in class 28611d have rank \(0\).
Complex multiplication
The elliptic curves in class 28611d do not have complex multiplication.Modular form 28611.2.a.d
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.