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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 185020.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185020.g1 | 185020i2 | \([0, -1, 0, -145981901, -681359624615]\) | \(-2259398347647852544/9735107421875\) | \(-1482411245304687500000000\) | \([]\) | \(30844800\) | \(3.4917\) | |
185020.g2 | 185020i1 | \([0, -1, 0, 4254339, -4935977639]\) | \(55923189948416/101442996875\) | \(-15447209035105311200000\) | \([]\) | \(10281600\) | \(2.9424\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 185020.g have rank \(0\).
Complex multiplication
The elliptic curves in class 185020.g do not have complex multiplication.Modular form 185020.2.a.g
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.