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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2496a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2496.h4 | 2496a1 | \([0, -1, 0, -53, 21]\) | \(16384000/9477\) | \(9704448\) | \([2]\) | \(384\) | \(0.030152\) | \(\Gamma_0(N)\)-optimal |
2496.h3 | 2496a2 | \([0, -1, 0, -593, 5745]\) | \(1409938000/4563\) | \(74760192\) | \([2]\) | \(768\) | \(0.37673\) | |
2496.h2 | 2496a3 | \([0, -1, 0, -2933, -60171]\) | \(2725888000000/19773\) | \(20247552\) | \([2]\) | \(1152\) | \(0.57946\) | |
2496.h1 | 2496a4 | \([0, -1, 0, -2993, -57519]\) | \(181037698000/14480427\) | \(237247315968\) | \([2]\) | \(2304\) | \(0.92603\) |
Rank
sage: E.rank()
The elliptic curves in class 2496a have rank \(1\).
Complex multiplication
The elliptic curves in class 2496a do not have complex multiplication.Modular form 2496.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.