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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2352.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2352.c1 | 2352d4 | \([0, -1, 0, -197584, 33870544]\) | \(7080974546692/189\) | \(22769316864\) | \([4]\) | \(9216\) | \(1.5011\) | |
2352.c2 | 2352d3 | \([0, -1, 0, -19224, -116640]\) | \(6522128932/3720087\) | \(448168463834112\) | \([2]\) | \(9216\) | \(1.5011\) | |
2352.c3 | 2352d2 | \([0, -1, 0, -12364, 530944]\) | \(6940769488/35721\) | \(1075850221824\) | \([2, 2]\) | \(4608\) | \(1.1546\) | |
2352.c4 | 2352d1 | \([0, -1, 0, -359, 17130]\) | \(-2725888/64827\) | \(-122029307568\) | \([2]\) | \(2304\) | \(0.80800\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2352.c have rank \(0\).
Complex multiplication
The elliptic curves in class 2352.c do not have complex multiplication.Modular form 2352.2.a.c
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.