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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 26520be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26520.bb2 | 26520be1 | \([0, 1, 0, -441593835, -5915392278642]\) | \(-595213448747095198927846967296/600281130562949295663181875\) | \(-9604498089007188730610910000\) | \([2]\) | \(15482880\) | \(4.0650\) | \(\Gamma_0(N)\)-optimal |
| 26520.bb1 | 26520be2 | \([0, 1, 0, -8285158460, -290175586566192]\) | \(245689277968779868090419995701456/93342399137270122585475925\) | \(23895654179141151381881836800\) | \([2]\) | \(30965760\) | \(4.4115\) |
Rank
sage: E.rank()
The elliptic curves in class 26520be have rank \(1\).
Complex multiplication
The elliptic curves in class 26520be do not have complex multiplication.Modular form 26520.2.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.
