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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 155526.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155526.u1 | 155526bx2 | \([1, 0, 1, -376395, 89304310]\) | \(-16591834777/98304\) | \(-34940600597446656\) | \([]\) | \(2280960\) | \(2.0147\) | |
155526.u2 | 155526bx1 | \([1, 0, 1, 12420, 654490]\) | \(596183/864\) | \(-307095122438496\) | \([]\) | \(760320\) | \(1.4654\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 155526.u have rank \(1\).
Complex multiplication
The elliptic curves in class 155526.u do not have complex multiplication.Modular form 155526.2.a.u
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.