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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 35904.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35904.b1 | 35904bw2 | \([0, -1, 0, -1148185, -473115239]\) | \(40869539953013031616/5226097476897\) | \(21406095265370112\) | \([2]\) | \(829440\) | \(2.1550\) | |
| 35904.b2 | 35904bw1 | \([0, -1, 0, -65620, -8694854]\) | \(-488268868033624384/230311020357297\) | \(-14739905302867008\) | \([2]\) | \(414720\) | \(1.8084\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35904.b have rank \(1\).
Complex multiplication
The elliptic curves in class 35904.b do not have complex multiplication.Modular form 35904.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
