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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 279312a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 279312.a1 | 279312a1 | \([0, -1, 0, -4240640, -3359792304]\) | \(55635379958596/24057\) | \(3646770566833152\) | \([2]\) | \(7983360\) | \(2.3285\) | \(\Gamma_0(N)\)-optimal |
| 279312.a2 | 279312a2 | \([0, -1, 0, -4219480, -3395002544]\) | \(-27403349188178/578739249\) | \(-175460719052610275328\) | \([2]\) | \(15966720\) | \(2.6750\) |
Rank
sage: E.rank()
The elliptic curves in class 279312a have rank \(0\).
Complex multiplication
The elliptic curves in class 279312a do not have complex multiplication.Modular form 279312.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
