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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 50575m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50575.t2 | 50575m1 | \([0, 1, 1, -9633, 400519]\) | \(-262144/35\) | \(-13200233046875\) | \([]\) | \(80640\) | \(1.2502\) | \(\Gamma_0(N)\)-optimal |
50575.t3 | 50575m2 | \([0, 1, 1, 62617, -1008356]\) | \(71991296/42875\) | \(-16170285482421875\) | \([]\) | \(241920\) | \(1.7995\) | |
50575.t1 | 50575m3 | \([0, 1, 1, -948883, -372481731]\) | \(-250523582464/13671875\) | \(-5156341033935546875\) | \([]\) | \(725760\) | \(2.3488\) |
Rank
sage: E.rank()
The elliptic curves in class 50575m have rank \(0\).
Complex multiplication
The elliptic curves in class 50575m do not have complex multiplication.Modular form 50575.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.