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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 92575.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92575.m1 | 92575n3 | \([0, -1, 1, -1736883, 922243293]\) | \(-250523582464/13671875\) | \(-31623877655029296875\) | \([]\) | \(1710720\) | \(2.4999\) | |
92575.m2 | 92575n1 | \([0, -1, 1, -17633, -993957]\) | \(-262144/35\) | \(-80957126796875\) | \([]\) | \(190080\) | \(1.4013\) | \(\Gamma_0(N)\)-optimal |
92575.m3 | 92575n2 | \([0, -1, 1, 114617, 2510668]\) | \(71991296/42875\) | \(-99172480326171875\) | \([]\) | \(570240\) | \(1.9506\) |
Rank
sage: E.rank()
The elliptic curves in class 92575.m have rank \(1\).
Complex multiplication
The elliptic curves in class 92575.m do not have complex multiplication.Modular form 92575.2.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 LMFDB numbering.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.