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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 361998.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361998.a1 | 361998a2 | \([1, -1, 0, -1500769971, 40226762824821]\) | \(-106237652098524394207033/137183418749137453056\) | \(-482713298836177837072230383616\) | \([]\) | \(498161664\) | \(4.3888\) | |
| 361998.a2 | 361998a1 | \([1, -1, 0, 156899484, -1057120174512]\) | \(121394948260111009847/207438591806724096\) | \(-729923250710536130648365056\) | \([]\) | \(166053888\) | \(3.8395\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 361998.a have rank \(1\).
Complex multiplication
The elliptic curves in class 361998.a do not have complex multiplication.Modular form 361998.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
