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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 466578d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466578.d2 | 466578d1 | \([1, -1, 0, -16879431, -26628746579]\) | \(2138072571/5488\) | \(1365176472686895700944\) | \([]\) | \(50872320\) | \(2.9316\) | \(\Gamma_0(N)\)-optimal* |
466578.d1 | 466578d2 | \([1, -1, 0, -79478646, 249705054836]\) | \(306177219/28672\) | \(5199483551810596393734144\) | \([]\) | \(152616960\) | \(3.4809\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 466578d have rank \(1\).
Complex multiplication
The elliptic curves in class 466578d do not have complex multiplication.Modular form 466578.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.