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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 37905b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37905.m4 | 37905b1 | \([1, 1, 0, 71832, -27841053]\) | \(871257511151/7637109375\) | \(-359294538840234375\) | \([2]\) | \(483840\) | \(2.0499\) | \(\Gamma_0(N)\)-optimal |
37905.m3 | 37905b2 | \([1, 1, 0, -1056293, -385907928]\) | \(2770485962938849/238901000625\) | \(11239308046184675625\) | \([2, 2]\) | \(967680\) | \(2.3965\) | |
37905.m2 | 37905b3 | \([1, 1, 0, -3628418, 2218625847]\) | \(112293400033564849/19723834261425\) | \(927925159526723440425\) | \([2]\) | \(1935360\) | \(2.7430\) | |
37905.m1 | 37905b4 | \([1, 1, 0, -16534168, -25884159203]\) | \(10625495353235512849/90517708575\) | \(4258485346012129575\) | \([2]\) | \(1935360\) | \(2.7430\) |
Rank
sage: E.rank()
The elliptic curves in class 37905b have rank \(0\).
Complex multiplication
The elliptic curves in class 37905b do not have complex multiplication.Modular form 37905.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.