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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 363888.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363888.dn1 | 363888dn1 | \([0, 0, 0, -19494, -925965]\) | \(55296/7\) | \(103712456480976\) | \([2]\) | \(1327104\) | \(1.4186\) | \(\Gamma_0(N)\)-optimal |
| 363888.dn2 | 363888dn2 | \([0, 0, 0, 29241, -4815018]\) | \(11664/49\) | \(-11615795125869312\) | \([2]\) | \(2654208\) | \(1.7652\) |
Rank
sage: E.rank()
The elliptic curves in class 363888.dn have rank \(0\).
Complex multiplication
The elliptic curves in class 363888.dn do not have complex multiplication.Modular form 363888.2.a.dn
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.
