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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 413820be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 413820.be1 | 413820be1 | \([0, 0, 0, -1003332, 360768881]\) | \(5405726654464/407253125\) | \(8415269859402450000\) | \([2]\) | \(8294400\) | \(2.3766\) | \(\Gamma_0(N)\)-optimal |
| 413820.be2 | 413820be2 | \([0, 0, 0, 962313, 1601877134]\) | \(298091207216/3525390625\) | \(-1165549842022500000000\) | \([2]\) | \(16588800\) | \(2.7232\) |
Rank
sage: E.rank()
The elliptic curves in class 413820be have rank \(2\).
Complex multiplication
The elliptic curves in class 413820be do not have complex multiplication.Modular form 413820.2.a.be
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
