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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 228752.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
228752.l1 | 228752j3 | \([0, 0, 0, -1220291, 518851586]\) | \(82483294977/17\) | \(41418737487872\) | \([2]\) | \(1548288\) | \(2.0002\) | |
228752.l2 | 228752j2 | \([0, 0, 0, -76531, 8048370]\) | \(20346417/289\) | \(704118537293824\) | \([2, 2]\) | \(774144\) | \(1.6536\) | |
228752.l3 | 228752j1 | \([0, 0, 0, -9251, -146334]\) | \(35937/17\) | \(41418737487872\) | \([2]\) | \(387072\) | \(1.3070\) | \(\Gamma_0(N)\)-optimal |
228752.l4 | 228752j4 | \([0, 0, 0, -9251, 21706210]\) | \(-35937/83521\) | \(-203490257277915136\) | \([2]\) | \(1548288\) | \(2.0002\) |
Rank
sage: E.rank()
The elliptic curves in class 228752.l have rank \(0\).
Complex multiplication
The elliptic curves in class 228752.l do not have complex multiplication.Modular form 228752.2.a.l
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.