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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 11025s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11025.bo2 | 11025s1 | \([0, 0, 1, -25725, -1725719]\) | \(-28672/3\) | \(-196994059171875\) | \([]\) | \(43008\) | \(1.4819\) | \(\Gamma_0(N)\)-optimal |
11025.bo1 | 11025s2 | \([0, 0, 1, -10058475, 12288393031]\) | \(-1713910976512/1594323\) | \(-104690719800360421875\) | \([]\) | \(559104\) | \(2.7644\) |
Rank
sage: E.rank()
The elliptic curves in class 11025s have rank \(0\).
Complex multiplication
The elliptic curves in class 11025s do not have complex multiplication.Modular form 11025.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.