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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 15925t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15925.l2 | 15925t1 | \([0, -1, 1, -4083, -91932]\) | \(163840/13\) | \(597436328125\) | \([]\) | \(17280\) | \(1.0033\) | \(\Gamma_0(N)\)-optimal |
15925.l1 | 15925t2 | \([0, -1, 1, -65333, 6431193]\) | \(671088640/2197\) | \(100966739453125\) | \([]\) | \(51840\) | \(1.5526\) |
Rank
sage: E.rank()
The elliptic curves in class 15925t have rank \(1\).
Complex multiplication
The elliptic curves in class 15925t do not have complex multiplication.Modular form 15925.2.a.t
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.