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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 62400dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62400.hx2 | 62400dc1 | \([0, 1, 0, 767, -175777]\) | \(7604375/2047032\) | \(-13415428915200\) | \([]\) | \(124416\) | \(1.1981\) | \(\Gamma_0(N)\)-optimal |
| 62400.hx1 | 62400dc2 | \([0, 1, 0, -215233, -38511457]\) | \(-168256703745625/30371328\) | \(-199041535180800\) | \([]\) | \(373248\) | \(1.7474\) |
Rank
sage: E.rank()
The elliptic curves in class 62400dc have rank \(1\).
Complex multiplication
The elliptic curves in class 62400dc do not have complex multiplication.Modular form 62400.2.a.dc
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.
