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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 154495b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154495.b4 | 154495b1 | \([1, -1, 1, 2282, 31996]\) | \(59319/55\) | \(-1219039862095\) | \([2]\) | \(151424\) | \(1.0063\) | \(\Gamma_0(N)\)-optimal |
| 154495.b3 | 154495b2 | \([1, -1, 1, -11763, 296042]\) | \(8120601/3025\) | \(67047192415225\) | \([2, 2]\) | \(302848\) | \(1.3529\) | |
| 154495.b1 | 154495b3 | \([1, -1, 1, -166258, 26127606]\) | \(22930509321/6875\) | \(152379982761875\) | \([2]\) | \(605696\) | \(1.6995\) | |
| 154495.b2 | 154495b4 | \([1, -1, 1, -81988, -8805118]\) | \(2749884201/73205\) | \(1622542056448445\) | \([2]\) | \(605696\) | \(1.6995\) |
Rank
sage: E.rank()
The elliptic curves in class 154495b have rank \(1\).
Complex multiplication
The elliptic curves in class 154495b do not have complex multiplication.Modular form 154495.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
