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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 2535e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2535.h2 | 2535e1 | \([0, 1, 1, 49799, 2237746]\) | \(16742875136/12301875\) | \(-10035017363401875\) | \([3]\) | \(14976\) | \(1.7587\) | \(\Gamma_0(N)\)-optimal |
| 2535.h1 | 2535e2 | \([0, 1, 1, -543391, -190489685]\) | \(-21752792449024/6591796875\) | \(-5377131217529296875\) | \([]\) | \(44928\) | \(2.3080\) |
Rank
sage: E.rank()
The elliptic curves in class 2535e have rank \(0\).
Complex multiplication
The elliptic curves in class 2535e do not have complex multiplication.Modular form 2535.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
