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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 18515l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18515.l2 | 18515l1 | \([0, 1, 1, -32445, 1976574]\) | \(48234496/6125\) | \(479654784846125\) | \([3]\) | \(75072\) | \(1.5461\) | \(\Gamma_0(N)\)-optimal |
18515.l1 | 18515l2 | \([0, 1, 1, -640795, -197379721]\) | \(371585744896/588245\) | \(46066045536621845\) | \([]\) | \(225216\) | \(2.0954\) |
Rank
sage: E.rank()
The elliptic curves in class 18515l have rank \(0\).
Complex multiplication
The elliptic curves in class 18515l do not have complex multiplication.Modular form 18515.2.a.l
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.