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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 195083.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
195083.m1 | 195083m2 | \([1, 0, 1, -148495, -22037199]\) | \(408023180713/1421\) | \(1261142730701\) | \([2]\) | \(734400\) | \(1.5414\) | |
195083.m2 | 195083m1 | \([1, 0, 1, -9150, -355117]\) | \(-95443993/5887\) | \(-5224734170047\) | \([2]\) | \(367200\) | \(1.1948\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 195083.m have rank \(0\).
Complex multiplication
The elliptic curves in class 195083.m do not have complex multiplication.Modular form 195083.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.