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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 11550.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11550.i1 | 11550f3 | \([1, 1, 0, -1232000, -526851000]\) | \(13235378341603461121/9240\) | \(144375000\) | \([2]\) | \(73728\) | \(1.7787\) | |
11550.i2 | 11550f2 | \([1, 1, 0, -77000, -8256000]\) | \(3231355012744321/85377600\) | \(1334025000000\) | \([2, 2]\) | \(36864\) | \(1.4321\) | |
11550.i3 | 11550f4 | \([1, 1, 0, -74000, -8925000]\) | \(-2868190647517441/527295615000\) | \(-8238993984375000\) | \([2]\) | \(73728\) | \(1.7787\) | |
11550.i4 | 11550f1 | \([1, 1, 0, -5000, -120000]\) | \(885012508801/127733760\) | \(1995840000000\) | \([2]\) | \(18432\) | \(1.0855\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11550.i have rank \(0\).
Complex multiplication
The elliptic curves in class 11550.i do not have complex multiplication.Modular form 11550.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.