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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 159120.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
159120.m1 | 159120du2 | \([0, 0, 0, -388623, -93244322]\) | \(34780972302198736/1711783125\) | \(319459813920000\) | \([2]\) | \(983040\) | \(1.8550\) | |
159120.m2 | 159120du1 | \([0, 0, 0, -22998, -1618697]\) | \(-115331093579776/30301171875\) | \(-353432868750000\) | \([2]\) | \(491520\) | \(1.5084\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 159120.m have rank \(1\).
Complex multiplication
The elliptic curves in class 159120.m do not have complex multiplication.Modular form 159120.2.a.m
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.