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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 18928m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18928.l2 | 18928m1 | \([0, -1, 0, 8056, 172912]\) | \(17303/14\) | \(-46777262465024\) | \([]\) | \(44928\) | \(1.3109\) | \(\Gamma_0(N)\)-optimal |
| 18928.l1 | 18928m2 | \([0, -1, 0, -167704, 26888432]\) | \(-156116857/2744\) | \(-9168343443144704\) | \([]\) | \(134784\) | \(1.8602\) |
Rank
sage: E.rank()
The elliptic curves in class 18928m have rank \(0\).
Complex multiplication
The elliptic curves in class 18928m do not have complex multiplication.Modular form 18928.2.a.m
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.
