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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 740.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 740.b1 | 740b2 | \([0, 1, 0, -12021, -511321]\) | \(750484394082304/578125\) | \(148000000\) | \([]\) | \(432\) | \(0.87559\) | |
| 740.b2 | 740b1 | \([0, 1, 0, -181, -425]\) | \(2575826944/1266325\) | \(324179200\) | \([3]\) | \(144\) | \(0.32628\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 740.b have rank \(1\).
Complex multiplication
The elliptic curves in class 740.b do not have complex multiplication.Modular form 740.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
