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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 485100b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 485100.b1 | 485100b1 | \([0, 0, 0, -190096725, 1019585636125]\) | \(-35431687725461248/440311012911\) | \(-9440941902739347057750000\) | \([]\) | \(134369280\) | \(3.6027\) | \(\Gamma_0(N)\)-optimal |
| 485100.b2 | 485100b2 | \([0, 0, 0, 661253775, 5210456705125]\) | \(1491325446082364672/1410025768453071\) | \(-30233110167566017551897750000\) | \([]\) | \(403107840\) | \(4.1521\) |
Rank
sage: E.rank()
The elliptic curves in class 485100b have rank \(0\).
Complex multiplication
The elliptic curves in class 485100b do not have complex multiplication.Modular form 485100.2.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 Cremona 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 Cremona labels.
