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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 308550.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308550.i1 | 308550i2 | \([1, 1, 0, -47431017845, 3975938166006525]\) | \(40037492117274604772994343/108243216\) | \(31903980154201782000\) | \([2]\) | \(551485440\) | \(4.3444\) | |
308550.i2 | 308550i1 | \([1, 1, 0, -2964437445, 62123158939725]\) | \(-9774766777004666957863/16072145144064\) | \(-4737159691482821394528000\) | \([2]\) | \(275742720\) | \(3.9979\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 308550.i have rank \(1\).
Complex multiplication
The elliptic curves in class 308550.i do not have complex multiplication.Modular form 308550.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.