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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 55825d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55825.l1 | 55825d1 | \([0, -1, 1, -1583, 37068]\) | \(-28094464000/20657483\) | \(-322773171875\) | \([]\) | \(48384\) | \(0.90779\) | \(\Gamma_0(N)\)-optimal |
55825.l2 | 55825d2 | \([0, -1, 1, 12917, -568307]\) | \(15252992000000/17621717267\) | \(-275339332296875\) | \([]\) | \(145152\) | \(1.4571\) |
Rank
sage: E.rank()
The elliptic curves in class 55825d have rank \(2\).
Complex multiplication
The elliptic curves in class 55825d do not have complex multiplication.Modular form 55825.2.a.d
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.