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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 144900m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
144900.j2 | 144900m1 | \([0, 0, 0, 240, 1325]\) | \(1048576/1127\) | \(-1643166000\) | \([2]\) | \(69120\) | \(0.45496\) | \(\Gamma_0(N)\)-optimal |
144900.j1 | 144900m2 | \([0, 0, 0, -1335, 12350]\) | \(11279504/3703\) | \(86383584000\) | \([2]\) | \(138240\) | \(0.80153\) |
Rank
sage: E.rank()
The elliptic curves in class 144900m have rank \(0\).
Complex multiplication
The elliptic curves in class 144900m do not have complex multiplication.Modular form 144900.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.