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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 155682m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155682.z2 | 155682m1 | \([1, -1, 1, 4144, -11277]\) | \(109503/64\) | \(-4600819082304\) | \([]\) | \(362880\) | \(1.1192\) | \(\Gamma_0(N)\)-optimal |
155682.z1 | 155682m2 | \([1, -1, 1, -53516, 5216563]\) | \(-35937/4\) | \(-1886623374937284\) | \([]\) | \(1088640\) | \(1.6685\) |
Rank
sage: E.rank()
The elliptic curves in class 155682m have rank \(1\).
Complex multiplication
The elliptic curves in class 155682m do not have complex multiplication.Modular form 155682.2.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.