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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 80937i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
80937.o2 | 80937i1 | \([0, 0, 1, 3174, -331551]\) | \(32768/459\) | \(-49534436854179\) | \([]\) | \(174240\) | \(1.3085\) | \(\Gamma_0(N)\)-optimal |
80937.o1 | 80937i2 | \([0, 0, 1, -282486, -57820626]\) | \(-23100424192/14739\) | \(-1590605805650859\) | \([]\) | \(522720\) | \(1.8578\) |
Rank
sage: E.rank()
The elliptic curves in class 80937i have rank \(1\).
Complex multiplication
The elliptic curves in class 80937i do not have complex multiplication.Modular form 80937.2.a.i
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.