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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 170014b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 170014.h2 | 170014b1 | \([1, -1, 1, 1320, 3995]\) | \(52734375/32192\) | \(-155384635328\) | \([2]\) | \(145152\) | \(0.83662\) | \(\Gamma_0(N)\)-optimal |
| 170014.h1 | 170014b2 | \([1, -1, 1, -5440, 36443]\) | \(3687953625/2024072\) | \(9769808946248\) | \([2]\) | \(290304\) | \(1.1832\) |
Rank
sage: E.rank()
The elliptic curves in class 170014b have rank \(1\).
Complex multiplication
The elliptic curves in class 170014b do not have complex multiplication.Modular form 170014.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
