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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 41070m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41070.p2 | 41070m1 | \([1, 0, 1, 30732652, 688165823378]\) | \(913923942103079/58773123072000\) | \(-206439387233170285965312000\) | \([3]\) | \(11988000\) | \(3.7289\) | \(\Gamma_0(N)\)-optimal |
41070.p1 | 41070m2 | \([1, 0, 1, -276984323, -18727790604802]\) | \(-669076050882037321/42749012087930880\) | \(-150155026634277685417192980480\) | \([]\) | \(35964000\) | \(4.2782\) |
Rank
sage: E.rank()
The elliptic curves in class 41070m have rank \(1\).
Complex multiplication
The elliptic curves in class 41070m do not have complex multiplication.Modular form 41070.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.