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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 74060.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
74060.m1 | 74060d1 | \([0, 1, 0, -1392756666, -20006497323991]\) | \(-126142795384287538429696/9315359375\) | \(-22064120102921750000\) | \([]\) | \(18703872\) | \(3.6080\) | \(\Gamma_0(N)\)-optimal |
74060.m2 | 74060d2 | \([0, 1, 0, -1378738166, -20428936569091]\) | \(-122372013839654770813696/5297595236711512175\) | \(-12547747526860066261767177200\) | \([]\) | \(56111616\) | \(4.1573\) |
Rank
sage: E.rank()
The elliptic curves in class 74060.m have rank \(1\).
Complex multiplication
The elliptic curves in class 74060.m do not have complex multiplication.Modular form 74060.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.