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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 25270.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25270.p1 | 25270t1 | \([1, 1, 1, -124011, -16862231]\) | \(-4483146738169/521360\) | \(-24527840518160\) | \([]\) | \(103680\) | \(1.5956\) | \(\Gamma_0(N)\)-optimal |
25270.p2 | 25270t2 | \([1, 1, 1, 14974, -51729777]\) | \(7892485271/24582656000\) | \(-1156512708839936000\) | \([]\) | \(311040\) | \(2.1449\) |
Rank
sage: E.rank()
The elliptic curves in class 25270.p have rank \(0\).
Complex multiplication
The elliptic curves in class 25270.p do not have complex multiplication.Modular form 25270.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.