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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 93138d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93138.e2 | 93138d1 | \([1, 1, 0, 57392, -11799296]\) | \(444369620591/1540767744\) | \(-72486775932862464\) | \([]\) | \(1206576\) | \(1.9182\) | \(\Gamma_0(N)\)-optimal |
93138.e1 | 93138d2 | \([1, 1, 0, -21624268, 38699970724]\) | \(-23769846831649063249/3261823333284\) | \(-153455352380702403204\) | \([]\) | \(8446032\) | \(2.8911\) |
Rank
sage: E.rank()
The elliptic curves in class 93138d have rank \(1\).
Complex multiplication
The elliptic curves in class 93138d do not have complex multiplication.Modular form 93138.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.