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SageMath
E = EllipticCurve("dw1")
E.isogeny_class()
Elliptic curves in class 37440.dw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37440.dw1 | 37440y1 | \([0, 0, 0, -87, 284]\) | \(42144192/4225\) | \(7300800\) | \([2]\) | \(6144\) | \(0.053229\) | \(\Gamma_0(N)\)-optimal |
37440.dw2 | 37440y2 | \([0, 0, 0, 108, 1376]\) | \(1259712/8125\) | \(-898560000\) | \([2]\) | \(12288\) | \(0.39980\) |
Rank
sage: E.rank()
The elliptic curves in class 37440.dw have rank \(1\).
Complex multiplication
The elliptic curves in class 37440.dw do not have complex multiplication.Modular form 37440.2.a.dw
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.