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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 116688.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116688.e1 | 116688p2 | \([0, -1, 0, -2973308, 2047856460]\) | \(-11355430171368393250000/498618024567704613\) | \(-127646214289332380928\) | \([]\) | \(2954880\) | \(2.6232\) | |
| 116688.e2 | 116688p1 | \([0, -1, 0, 185692, 7748988]\) | \(2766056134796750000/1703681184259197\) | \(-436142383170354432\) | \([]\) | \(984960\) | \(2.0739\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116688.e have rank \(0\).
Complex multiplication
The elliptic curves in class 116688.e do not have complex multiplication.Modular form 116688.2.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 LMFDB 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 LMFDB labels.
