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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 78897.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78897.d1 | 78897b1 | \([1, 1, 1, -131501, 18289946]\) | \(10418796526321/6390657\) | \(154254924292833\) | \([2]\) | \(645120\) | \(1.6653\) | \(\Gamma_0(N)\)-optimal |
78897.d2 | 78897b2 | \([1, 1, 1, -106936, 25364666]\) | \(-5602762882081/8312741073\) | \(-200649361228671537\) | \([2]\) | \(1290240\) | \(2.0118\) |
Rank
sage: E.rank()
The elliptic curves in class 78897.d have rank \(0\).
Complex multiplication
The elliptic curves in class 78897.d do not have complex multiplication.Modular form 78897.2.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 LMFDB 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 LMFDB labels.