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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 379456.cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
379456.cd1 | 379456cd2 | \([0, 1, 0, -793921, 272012607]\) | \(1389715708/11\) | \(438049154859008\) | \([2]\) | \(5898240\) | \(1.9820\) | |
379456.cd2 | 379456cd1 | \([0, 1, 0, -48561, 4428367]\) | \(-1272112/121\) | \(-1204635175862272\) | \([2]\) | \(2949120\) | \(1.6354\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 379456.cd have rank \(0\).
Complex multiplication
The elliptic curves in class 379456.cd do not have complex multiplication.Modular form 379456.2.a.cd
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.