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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 2790f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2790.g2 | 2790f1 | \([1, -1, 0, 561, 1773]\) | \(722458663317/476656000\) | \(-12869712000\) | \([3]\) | \(2016\) | \(0.62865\) | \(\Gamma_0(N)\)-optimal |
2790.g1 | 2790f2 | \([1, -1, 0, -6414, -230572]\) | \(-1482713947827/325058560\) | \(-6398127636480\) | \([]\) | \(6048\) | \(1.1780\) |
Rank
sage: E.rank()
The elliptic curves in class 2790f have rank \(1\).
Complex multiplication
The elliptic curves in class 2790f do not have complex multiplication.Modular form 2790.2.a.f
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.