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SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 331200gb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 331200.gb2 | 331200gb1 | \([0, 0, 0, -21900, -1008880]\) | \(243135625/48668\) | \(232514990899200\) | \([]\) | \(663552\) | \(1.4728\) | \(\Gamma_0(N)\)-optimal |
| 331200.gb1 | 331200gb2 | \([0, 0, 0, -1677900, -836560240]\) | \(109348914285625/1472\) | \(7032589516800\) | \([]\) | \(1990656\) | \(2.0221\) |
Rank
sage: E.rank()
The elliptic curves in class 331200gb have rank \(1\).
Complex multiplication
The elliptic curves in class 331200gb do not have complex multiplication.Modular form 331200.2.a.gb
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.
