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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 30015l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30015.j2 | 30015l1 | \([0, 0, 1, -1116192, -404445195]\) | \(210966209738334797824/25153051046653125\) | \(18336574213010128125\) | \([]\) | \(518400\) | \(2.4273\) | \(\Gamma_0(N)\)-optimal |
| 30015.j1 | 30015l2 | \([0, 0, 1, -21411552, 38076762402]\) | \(1489157481162281146384384/2616603057861328125\) | \(1907503629180908203125\) | \([3]\) | \(1555200\) | \(2.9766\) |
Rank
sage: E.rank()
The elliptic curves in class 30015l have rank \(0\).
Complex multiplication
The elliptic curves in class 30015l do not have complex multiplication.Modular form 30015.2.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.
