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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 152880.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152880.l1 | 152880dz2 | \([0, -1, 0, -1365156, 396727500]\) | \(9342060412991056/3153896484375\) | \(94989508477500000000\) | \([2]\) | \(4976640\) | \(2.5357\) | |
152880.l2 | 152880dz1 | \([0, -1, 0, 249639, 42764436]\) | \(914010221133824/950278021875\) | \(-1788788143929150000\) | \([2]\) | \(2488320\) | \(2.1891\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152880.l have rank \(0\).
Complex multiplication
The elliptic curves in class 152880.l do not have complex multiplication.Modular form 152880.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.