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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 3248.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3248.d1 | 3248h2 | \([0, 1, 0, -2472, -48140]\) | \(408023180713/1421\) | \(5820416\) | \([2]\) | \(1536\) | \(0.51751\) | |
| 3248.d2 | 3248h1 | \([0, 1, 0, -152, -812]\) | \(-95443993/5887\) | \(-24113152\) | \([2]\) | \(768\) | \(0.17094\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3248.d have rank \(0\).
Complex multiplication
The elliptic curves in class 3248.d do not have complex multiplication.Modular form 3248.2.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.
