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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 119952.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 119952.dn1 | 119952s1 | \([0, 0, 0, -21315, 1184722]\) | \(12194500/153\) | \(13437149709312\) | \([2]\) | \(184320\) | \(1.3285\) | \(\Gamma_0(N)\)-optimal |
| 119952.dn2 | 119952s2 | \([0, 0, 0, -3675, 3086314]\) | \(-31250/23409\) | \(-4111767811049472\) | \([2]\) | \(368640\) | \(1.6751\) |
Rank
sage: E.rank()
The elliptic curves in class 119952.dn have rank \(1\).
Complex multiplication
The elliptic curves in class 119952.dn do not have complex multiplication.Modular form 119952.2.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.
