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SageMath
E = EllipticCurve("ccn1")
E.isogeny_class()
Elliptic curves in class 705600.ccn
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.ccn1 | \([0, 0, 0, -101271607500, 12404511585830000]\) | \(266916252066900625/162\) | \(69715094374195200000000\) | \([]\) | \(1393459200\) | \(4.6059\) |
| 705600.ccn2 | \([0, 0, 0, -1252807500, 16943160710000]\) | \(505318200625/4251528\) | \(1829602936756378828800000000\) | \([]\) | \(464486400\) | \(4.0566\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.ccn have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.ccn do not have complex multiplication.Modular form 705600.2.a.ccn
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
