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SageMath
E = EllipticCurve("iv1")
E.isogeny_class()
Elliptic curves in class 278850.iv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
278850.iv1 | 278850iv2 | \([1, 0, 0, -68160830813, -6849372486091383]\) | \(464352938845529653759213009/2445173327025000\) | \(184412259710065831640625000\) | \([2]\) | \(650280960\) | \(4.6567\) | |
278850.iv2 | 278850iv1 | \([1, 0, 0, -4257705813, -107145476716383]\) | \(-113180217375258301213009/260161419375000000\) | \(-19621085632687880859375000000\) | \([2]\) | \(325140480\) | \(4.3101\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 278850.iv have rank \(1\).
Complex multiplication
The elliptic curves in class 278850.iv do not have complex multiplication.Modular form 278850.2.a.iv
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.