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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 18032.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18032.d1 | 18032v2 | \([0, 1, 0, -2692664, 1699777876]\) | \(13062552753151/92\) | \(15206530433024\) | \([2]\) | \(172032\) | \(2.1275\) | |
| 18032.d2 | 18032v1 | \([0, 1, 0, -168184, 26552532]\) | \(-3183010111/8464\) | \(-1399000799838208\) | \([2]\) | \(86016\) | \(1.7810\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18032.d have rank \(1\).
Complex multiplication
The elliptic curves in class 18032.d do not have complex multiplication.Modular form 18032.2.a.d
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.
