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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 38025l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38025.ba2 | 38025l1 | \([1, -1, 1, -919730, 378620272]\) | \(-57960603/8125\) | \(-12061318946396484375\) | \([2]\) | \(774144\) | \(2.3927\) | \(\Gamma_0(N)\)-optimal |
| 38025.ba1 | 38025l2 | \([1, -1, 1, -15179105, 22765839022]\) | \(260549802603/4225\) | \(6271885852126171875\) | \([2]\) | \(1548288\) | \(2.7393\) |
Rank
sage: E.rank()
The elliptic curves in class 38025l have rank \(1\).
Complex multiplication
The elliptic curves in class 38025l do not have complex multiplication.Modular form 38025.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
