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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 361998d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
361998.d1 | 361998d1 | \([1, -1, 0, -307098, 65598196]\) | \(-1999852137736669/636095936\) | \(-1018779520344768\) | \([]\) | \(3024000\) | \(1.8549\) | \(\Gamma_0(N)\)-optimal |
361998.d2 | 361998d2 | \([1, -1, 0, 1950417, -195921491]\) | \(512328390183400211/306788440211456\) | \(-491356354092390678528\) | \([]\) | \(15120000\) | \(2.6596\) |
Rank
sage: E.rank()
The elliptic curves in class 361998d have rank \(2\).
Complex multiplication
The elliptic curves in class 361998d do not have complex multiplication.Modular form 361998.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.