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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 99275a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 99275.e3 | 99275a1 | \([1, -1, 0, -8866242917, 321336861942616]\) | \(104857852278310619039721/47155625\) | \(34663717534853515625\) | \([2]\) | \(38154240\) | \(3.9928\) | \(\Gamma_0(N)\)-optimal |
| 99275.e2 | 99275a2 | \([1, -1, 0, -8866288042, 321333427523991]\) | \(104859453317683374662841/2223652969140625\) | \(1634589265179476812744140625\) | \([2, 2]\) | \(76308480\) | \(4.3393\) | |
| 99275.e4 | 99275a3 | \([1, -1, 0, -8556775667, 344807774581116]\) | \(-94256762600623910012361/15323275604248046875\) | \(-11264015634494636058807373046875\) | \([2]\) | \(152616960\) | \(4.6859\) | |
| 99275.e1 | 99275a4 | \([1, -1, 0, -9176522417, 297639277133366]\) | \(116256292809537371612841/15216540068579856875\) | \(11185555207783434149035654296875\) | \([2]\) | \(152616960\) | \(4.6859\) |
Rank
sage: E.rank()
The elliptic curves in class 99275a have rank \(0\).
Complex multiplication
The elliptic curves in class 99275a do not have complex multiplication.Modular form 99275.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
