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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 487872da
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
487872.da2 | 487872da1 | \([0, 0, 0, 18876, -244904]\) | \(15185664/9317\) | \(-456347764325376\) | \([]\) | \(2211840\) | \(1.5020\) | \(\Gamma_0(N)\)-optimal |
487872.da1 | 487872da2 | \([0, 0, 0, -300564, -65836584]\) | \(-84098304/3773\) | \(-134720648673278976\) | \([]\) | \(6635520\) | \(2.0513\) |
Rank
sage: E.rank()
The elliptic curves in class 487872da have rank \(2\).
Complex multiplication
The elliptic curves in class 487872da do not have complex multiplication.Modular form 487872.2.a.da
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.