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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 26010.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26010.g1 | 26010f4 | \([1, -1, 0, -483840, 129389206]\) | \(711882749089/1721250\) | \(30287610377471250\) | \([2]\) | \(294912\) | \(2.0413\) | |
26010.g2 | 26010f3 | \([1, -1, 0, -431820, -108643910]\) | \(506071034209/2505630\) | \(44089786602819630\) | \([2]\) | \(294912\) | \(2.0413\) | |
26010.g3 | 26010f2 | \([1, -1, 0, -41670, 364000]\) | \(454756609/260100\) | \(4576794457040100\) | \([2, 2]\) | \(147456\) | \(1.6947\) | |
26010.g4 | 26010f1 | \([1, -1, 0, 10350, 41476]\) | \(6967871/4080\) | \(-71792854228080\) | \([2]\) | \(73728\) | \(1.3481\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26010.g have rank \(0\).
Complex multiplication
The elliptic curves in class 26010.g do not have complex multiplication.Modular form 26010.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.