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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 463680.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
463680.d1 | 463680d1 | \([0, 0, 0, -82634268, 289123605808]\) | \(5224645130090610708304/67370009765625\) | \(804663084960000000000\) | \([2]\) | \(55050240\) | \(3.1566\) | \(\Gamma_0(N)\)-optimal |
463680.d2 | 463680d2 | \([0, 0, 0, -80384268, 305610705808]\) | \(-1202345928696155427076/148724718496003125\) | \(-7105434077337110323200000\) | \([2]\) | \(110100480\) | \(3.5031\) |
Rank
sage: E.rank()
The elliptic curves in class 463680.d have rank \(1\).
Complex multiplication
The elliptic curves in class 463680.d do not have complex multiplication.Modular form 463680.2.a.d
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.