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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 228718d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
228718.t2 | 228718d1 | \([1, 0, 0, -17318, 871840]\) | \(647214625/3332\) | \(2957162265092\) | \([2]\) | \(491520\) | \(1.2388\) | \(\Gamma_0(N)\)-optimal |
228718.t1 | 228718d2 | \([1, 0, 0, -26928, -206402]\) | \(2433138625/1387778\) | \(1231658083410818\) | \([2]\) | \(983040\) | \(1.5854\) |
Rank
sage: E.rank()
The elliptic curves in class 228718d have rank \(0\).
Complex multiplication
The elliptic curves in class 228718d do not have complex multiplication.Modular form 228718.2.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.